Finite Group Databasebeta

← Group #188602

Character table — Group #188602

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222222222444444448888888888888888888888881111111122222222222244444444888888888888888888888888
order12222222444444444444444444442222444488888888888888882222222244444444444444444444222244448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11111111-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11111111-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-22222-2-22-2-2-2-222-2-200000000000000000000000022222222222-2-22222-2-22-2-2-2-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-22-2-222-2-22200000000000000000000000022222222222-2-2-2-2-2-2-2-22-2-222-2-222000000000000000000000000
χ1922222222-2-2-222222222-2-2-2-2-2-2-22200000000000000000000000022222222-2-2-222222222-2-2-2-2-2-2-222000000000000000000000000
χ2022222222-2-2-222-2-2-2-222-2-2-22222-2-200000000000000000000000022222222-2-2-222-2-2-2-222-2-2-22222-2-2000000000000000000000000
χ212222-2-2-2-20002-22i2i−2i−2i2-200000002i−2i00000000000000002−22−2i2−i2i2−i22222-2-2-2-20002-22i2i−2i−2i2-200000002i−2i00000000000000002−22−2i2−i2i2−i2
χ222222-2-2-2-20002-22i2i−2i−2i2-200000002i−2i0000000000000000−22−22−i2i2−i2i22222-2-2-2-20002-22i2i−2i−2i2-200000002i−2i0000000000000000−22−22−i2i2−i2i2
χ232222-2-2-2-20002-2−2i−2i2i2i2-20000000−2i2i00000000000000002−22−2−i2i2−i2i22222-2-2-2-20002-2−2i−2i2i2i2-20000000−2i2i00000000000000002−22−2−i2i2−i2i2
χ242222-2-2-2-20002-2−2i−2i2i2i2-20000000−2i2i0000000000000000−22−22i2−i2i2−i22222-2-2-2-20002-2−2i−2i2i2i2-20000000−2i2i0000000000000000−22−22i2−i2i2−i2
χ252222-2-2-2-2000-222i2i−2i−2i-220000000−2i2i0000000000000000i2−i2−i2i2−222−22222-2-2-2-2000-222i2i−2i−2i-220000000−2i2i0000000000000000i2−i2−i2i2−222−2
χ262222-2-2-2-2000-222i2i−2i−2i-220000000−2i2i0000000000000000−i2i2i2−i22−2−222222-2-2-2-2000-222i2i−2i−2i-220000000−2i2i0000000000000000−i2i2i2−i22−2−22
χ272222-2-2-2-2000-22−2i−2i2i2i-2200000002i−2i0000000000000000i2−i2−i2i22−2−222222-2-2-2-2000-22−2i−2i2i2i-2200000002i−2i0000000000000000i2−i2−i2i22−2−22
χ282222-2-2-2-2000-22−2i−2i2i2i-2200000002i−2i0000000000000000−i2i2i2−i2−222−22222-2-2-2-2000-22−2i−2i2i2i-2200000002i−2i0000000000000000−i2i2i2−i2−222−2
χ2922-2-222-2-222-2220000-2-2-22-20000002-22-20000000000000000000022-2-222-2-222-2220000-2-2-22-20000002-22-200000000000000000000
χ3022-2-222-2-222-2220000-2-2-22-2000000-22-220000000000000000000022-2-222-2-222-2220000-2-2-22-2000000-22-2200000000000000000000
χ3122-2-222-2-222-2-2-2000022-2-2200000000002i−2i2i−2i000000000000000022-2-222-2-222-2-2-2000022-2-2200000000002i−2i2i−2i0000000000000000
χ3222-2-222-2-222-2-2-2000022-2-220000000000−2i2i−2i2i000000000000000022-2-222-2-222-2-2-2000022-2-220000000000−2i2i−2i2i0000000000000000
χ3322-2-222-2-2-2-22220000-2-22-2200000000002i−2i−2i2i000000000000000022-2-222-2-2-2-22220000-2-22-2200000000002i−2i−2i2i0000000000000000
χ3422-2-222-2-2-2-22220000-2-22-220000000000−2i2i2i−2i000000000000000022-2-222-2-2-2-22220000-2-22-220000000000−2i2i2i−2i0000000000000000
χ3522-2-222-2-2-2-22-2-200002222-20000002-2-220000000000000000000022-2-222-2-2-2-22-2-200002222-20000002-2-2200000000000000000000
χ3622-2-222-2-2-2-22-2-200002222-2000000-222-20000000000000000000022-2-222-2-2-2-22-2-200002222-2000000-222-200000000000000000000
χ372-22-22-2-222-22002-22-200-200002-20000000000i2−i2i2−i2i2−i2i2−i2000000002-22-22-2-222-22002-22-200-200002-20000000000i2−i2i2−i2i2−i2i2−i200000000
χ382-22-22-2-222-22002-22-200-200002-20000000000−i2i2−i2i2−i2i2−i2i2000000002-22-22-2-222-22002-22-200-200002-20000000000−i2i2−i2i2−i2i2−i2i200000000
χ392-22-22-2-222-2200-22-2200-20000-220000000000i2−i2i2−i2−i2i2−i2i2000000002-22-22-2-222-2200-22-2200-20000-220000000000i2−i2i2−i2−i2i2−i2i200000000
χ402-22-22-2-222-2200-22-2200-20000-220000000000−i2i2−i2i2i2−i2i2−i2000000002-22-22-2-222-2200-22-2200-20000-220000000000−i2i2−i2i2i2−i2i2−i200000000
χ412-22-22-2-22-22-2002-22-20020000-2200000000002−2−222−2−22000000002-22-22-2-22-22-2002-22-20020000-2200000000002−2−222−2−2200000000
χ422-22-22-2-22-22-2002-22-20020000-220000000000−222−2−222−2000000002-22-22-2-22-22-2002-22-20020000-220000000000−222−2−222−200000000
χ432-22-22-2-22-22-200-22-2200200002-200000000002−2−22−222−2000000002-22-22-2-22-22-200-22-2200200002-200000000002−2−22−222−200000000
χ442-22-22-2-22-22-200-22-2200200002-20000000000−222−22−2−22000000002-22-22-2-22-22-200-22-2200200002-20000000000−222−22−2−2200000000
χ4544-4-4-4-4440004-40000-4400000000000000000000000000000000044-4-4-4-4440004-40000-44000000000000000000000000000000000
χ4644-4-4-4-444000-4400004-400000000000000000000000000000000044-4-4-4-444000-4400004-4000000000000000000000000000000000
χ474-44-4-444-4000004i−4i−4i4i000000000000000000000000000000000004-44-4-444-4000004i−4i−4i4i00000000000000000000000000000000000
χ484-44-4-444-400000−4i4i4i−4i000000000000000000000000000000000004-44-4-444-400000−4i4i4i−4i00000000000000000000000000000000000
χ494-4-444-44-44-4-4000000004000000000000000000000000000000004-4-444-44-44-4-400000000400000000000000000000000000000000
χ504-4-444-44-4-44400000000-4000000000000000000000000000000004-4-444-44-4-44400000000-400000000000000000000000000000000
χ514-4-44-44-44000000000000004-400000000000000000000000000004-4-44-44-44000000000000004-40000000000000000000000000000
χ524-4-44-44-4400000000000000-4400000000000000000000000000004-4-44-44-4400000000000000-440000000000000000000000000000
χ531111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ54111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ551111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ561111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ571111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ581111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ591111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ601111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ6211111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ6311111111-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1111111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ6411111111-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1111111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ6511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ6611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ6711111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ6811111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ6922222222222-2-22222-2-22-2-2-2-222-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222-22222-2-222000000000000000000000000
χ7022222222222-2-2-2-2-2-2-2-22-2-222-2-222000000000000000000000000-2-2-2-2-2-2-2-2-2-2-222222222-222-2-222-2-2000000000000000000000000
χ7122222222-2-2-222222222-2-2-2-2-2-2-222000000000000000000000000-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22222222-2-2000000000000000000000000
χ7222222222-2-2-222-2-2-2-222-2-2-22222-2-2000000000000000000000000-2-2-2-2-2-2-2-2222-2-22222-2-2222-2-2-2-222000000000000000000000000
χ732222-2-2-2-20002-22i2i−2i−2i2-200000002i−2i00000000000000002−22−2i2−i2i2−i2-2-2-2-22222000-22−2i−2i2i2i-220000000−2i2i0000000000000000−22−22−i2i2−i2i2
χ742222-2-2-2-20002-22i2i−2i−2i2-200000002i−2i0000000000000000−22−22−i2i2−i2i2-2-2-2-22222000-22−2i−2i2i2i-220000000−2i2i00000000000000002−22−2i2−i2i2−i2
χ752222-2-2-2-20002-2−2i−2i2i2i2-20000000−2i2i00000000000000002−22−2−i2i2−i2i2-2-2-2-22222000-222i2i−2i−2i-2200000002i−2i0000000000000000−22−22i2−i2i2−i2
χ762222-2-2-2-20002-2−2i−2i2i2i2-20000000−2i2i0000000000000000−22−22i2−i2i2−i2-2-2-2-22222000-222i2i−2i−2i-2200000002i−2i00000000000000002−22−2−i2i2−i2i2
χ772222-2-2-2-2000-222i2i−2i−2i-220000000−2i2i0000000000000000i2−i2−i2i2−222−2-2-2-2-222220002-2−2i−2i2i2i2-200000002i−2i0000000000000000−i2i2i2−i22−2−22
χ782222-2-2-2-2000-222i2i−2i−2i-220000000−2i2i0000000000000000−i2i2i2−i22−2−22-2-2-2-222220002-2−2i−2i2i2i2-200000002i−2i0000000000000000i2−i2−i2i2−222−2
χ792222-2-2-2-2000-22−2i−2i2i2i-2200000002i−2i0000000000000000i2−i2−i2i22−2−22-2-2-2-222220002-22i2i−2i−2i2-20000000−2i2i0000000000000000−i2i2i2−i2−222−2
χ802222-2-2-2-2000-22−2i−2i2i2i-2200000002i−2i0000000000000000−i2i2i2−i2−222−2-2-2-2-222220002-22i2i−2i−2i2-20000000−2i2i0000000000000000i2−i2−i2i22−2−22
χ8122-2-222-2-222-2220000-2-2-22-20000002-22-200000000000000000000-2-222-2-222-2-22-2-20000222-22000000-22-2200000000000000000000
χ8222-2-222-2-222-2220000-2-2-22-2000000-22-2200000000000000000000-2-222-2-222-2-22-2-20000222-220000002-22-200000000000000000000
χ8322-2-222-2-222-2-2-2000022-2-2200000000002i−2i2i−2i0000000000000000-2-222-2-222-2-22220000-2-222-20000000000−2i2i−2i2i0000000000000000
χ8422-2-222-2-222-2-2-2000022-2-220000000000−2i2i−2i2i0000000000000000-2-222-2-222-2-22220000-2-222-200000000002i−2i2i−2i0000000000000000
χ8522-2-222-2-2-2-22220000-2-22-2200000000002i−2i−2i2i0000000000000000-2-222-2-22222-2-2-2000022-22-20000000000−2i2i2i−2i0000000000000000
χ8622-2-222-2-2-2-22220000-2-22-220000000000−2i2i2i−2i0000000000000000-2-222-2-22222-2-2-2000022-22-200000000002i−2i−2i2i0000000000000000
χ8722-2-222-2-2-2-22-2-200002222-20000002-2-2200000000000000000000-2-222-2-22222-2220000-2-2-2-22000000-222-200000000000000000000
χ8822-2-222-2-2-2-22-2-200002222-2000000-222-200000000000000000000-2-222-2-22222-2220000-2-2-2-220000002-2-2200000000000000000000
χ892-22-22-2-222-22002-22-200-200002-20000000000i2−i2i2−i2i2−i2i2−i200000000-22-22-222-2-22-200-22-220020000-220000000000−i2i2−i2i2−i2i2−i2i200000000
χ902-22-22-2-222-22002-22-200-200002-20000000000−i2i2−i2i2−i2i2−i2i200000000-22-22-222-2-22-200-22-220020000-220000000000i2−i2i2−i2i2−i2i2−i200000000
χ912-22-22-2-222-2200-22-2200-20000-220000000000i2−i2i2−i2−i2i2−i2i200000000-22-22-222-2-22-2002-22-200200002-20000000000−i2i2−i2i2i2−i2i2−i200000000
χ922-22-22-2-222-2200-22-2200-20000-220000000000−i2i2−i2i2i2−i2i2−i200000000-22-22-222-2-22-2002-22-200200002-20000000000i2−i2i2−i2−i2i2−i2i200000000
χ932-22-22-2-22-22-2002-22-20020000-2200000000002−2−222−2−2200000000-22-22-222-22-2200-22-2200-200002-20000000000−222−2−222−200000000
χ942-22-22-2-22-22-2002-22-20020000-220000000000−222−2−222−200000000-22-22-222-22-2200-22-2200-200002-200000000002−2−222−2−2200000000
χ952-22-22-2-22-22-200-22-2200200002-200000000002−2−22−222−200000000-22-22-222-22-22002-22-200-20000-220000000000−222−22−2−2200000000
χ962-22-22-2-22-22-200-22-2200200002-20000000000−222−22−2−2200000000-22-22-222-22-22002-22-200-20000-2200000000002−2−22−222−200000000
χ9744-4-4-4-4440004-40000-44000000000000000000000000000000000-4-44444-4-4000-4400004-4000000000000000000000000000000000
χ9844-4-4-4-444000-4400004-4000000000000000000000000000000000-4-44444-4-40004-40000-44000000000000000000000000000000000
χ994-44-4-444-4000004i−4i−4i4i00000000000000000000000000000000000-44-444-4-4400000−4i4i4i−4i00000000000000000000000000000000000
χ1004-44-4-444-400000−4i4i4i−4i00000000000000000000000000000000000-44-444-4-44000004i−4i−4i4i00000000000000000000000000000000000
χ1014-4-444-44-44-4-400000000400000000000000000000000000000000-444-4-44-44-44400000000-400000000000000000000000000000000
χ1024-4-444-44-4-44400000000-400000000000000000000000000000000-444-4-44-444-4-400000000400000000000000000000000000000000
χ1034-4-44-44-44000000000000004-40000000000000000000000000000-444-44-44-400000000000000-440000000000000000000000000000
χ1044-4-44-44-4400000000000000-440000000000000000000000000000-444-44-44-4000000000000004-40000000000000000000000000000

Here i is the imaginary unit (i² = −1).