Finite Group Databasebeta

← Group #188604

Character table — Group #188604

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222222222444444448888888888888888888888881111111122222222222244444444888888888888888888888888
order12222222444444444444444444444444444488888888888888882222222244444444444444444444444444448888888888888888
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
χ5111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-11111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
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
χ1722222222222222-2-2-222-2-2-2-2-222-2-200000000000000000000000022222222222222-2-2-222-2-2-2-2-222-2-2000000000000000000000000
χ18222222222222-2-2222-2-22-2-2-2-2-2-222000000000000000000000000222222222222-2-2222-2-22-2-2-2-2-2-222000000000000000000000000
χ1922222222-2-2-2-222-2-2-222-2-2-222-2-22200000000000000000000000022222222-2-2-2-222-2-2-222-2-2-222-2-222000000000000000000000000
χ2022222222-2-2-2-2-2-2222-2-22-2-22222-2-200000000000000000000000022222222-2-2-2-2-2-2222-2-22-2-22222-2-2000000000000000000000000
χ21222-2-2-22-200002222-2-2-2-22-2000000002-2002-20000000000000000222-2-2-22-200002222-2-2-2-22-2000000002-2002-20000000000000000
χ22222-2-2-22-200002222-2-2-2-22-200000000-2200-220000000000000000222-2-2-22-200002222-2-2-2-22-200000000-2200-220000000000000000
χ23222-2-2-22-2000022-2-22-2-22-220000002i−2i002i−2i000000000000000000222-2-2-22-2000022-2-22-2-22-220000002i−2i002i−2i000000000000000000
χ24222-2-2-22-2000022-2-22-2-22-22000000−2i2i00−2i2i000000000000000000222-2-2-22-2000022-2-22-2-22-22000000−2i2i00−2i2i000000000000000000
χ25222-2-2-22-20000-2-222-222-2-220000002i−2i00−2i2i000000000000000000222-2-2-22-20000-2-222-222-2-220000002i−2i00−2i2i000000000000000000
χ26222-2-2-22-20000-2-222-222-2-22000000−2i2i002i−2i000000000000000000222-2-2-22-20000-2-222-222-2-22000000−2i2i002i−2i000000000000000000
χ27222-2-2-22-20000-2-2-2-222222-2000000002-200-220000000000000000222-2-2-22-20000-2-2-2-222222-2000000002-200-220000000000000000
χ28222-2-2-22-20000-2-2-2-222222-200000000-22002-20000000000000000222-2-2-22-20000-2-2-2-222222-200000000-22002-20000000000000000
χ2922-22-2-2-222i2i−2i−2i2-20002-2000002i−2i0000000000000000002−2i2−i22−2i2−i222-22-2-2-222i2i−2i−2i2-20002-2000002i−2i0000000000000000002−2i2−i22−2i2−i2
χ3022-22-2-2-222i2i−2i−2i2-20002-2000002i−2i000000000000000000−22−i2i2−22−i2i222-22-2-2-222i2i−2i−2i2-20002-2000002i−2i000000000000000000−22−i2i2−22−i2i2
χ3122-22-2-2-222i2i−2i−2i-22000-2200000−2i2i000000000000000000i2−i2−22−i2i22−222-22-2-2-222i2i−2i−2i-22000-2200000−2i2i000000000000000000i2−i2−22−i2i22−2
χ3222-22-2-2-222i2i−2i−2i-22000-2200000−2i2i000000000000000000−i2i22−2i2−i2−2222-22-2-2-222i2i−2i−2i-22000-2200000−2i2i000000000000000000−i2i22−2i2−i2−22
χ3322-22-2-2-22−2i−2i2i2i2-20002-200000−2i2i0000000000000000002−2−i2i22−2−i2i222-22-2-2-22−2i−2i2i2i2-20002-200000−2i2i0000000000000000002−2−i2i22−2−i2i2
χ3422-22-2-2-22−2i−2i2i2i2-20002-200000−2i2i000000000000000000−22i2−i2−22i2−i222-22-2-2-22−2i−2i2i2i2-20002-200000−2i2i000000000000000000−22i2−i2−22i2−i2
χ3522-22-2-2-22−2i−2i2i2i-22000-22000002i−2i000000000000000000i2−i22−2−i2i2−2222-22-2-2-22−2i−2i2i2i-22000-22000002i−2i000000000000000000i2−i22−2−i2i2−22
χ3622-22-2-2-22−2i−2i2i2i-22000-22000002i−2i000000000000000000−i2i2−22i2−i22−222-22-2-2-22−2i−2i2i2i-22000-22000002i−2i000000000000000000−i2i2−22i2−i22−2
χ372-2-2-22-2222-22-2002-2200-20000002-200000000i2−i2i2−i2i2−i2i2−i2000000002-2-2-22-2222-22-2002-2200-20000002-200000000i2−i2i2−i2i2−i2i2−i200000000
χ382-2-2-22-2222-22-2002-2200-20000002-200000000−i2i2−i2i2−i2i2−i2i2000000002-2-2-22-2222-22-2002-2200-20000002-200000000−i2i2−i2i2−i2i2−i2i200000000
χ392-2-2-22-2222-22-200-22-2002000000-22000000002−22−2−22−22000000002-2-2-22-2222-22-200-22-2002000000-22000000002−22−2−22−2200000000
χ402-2-2-22-2222-22-200-22-2002000000-2200000000−22−222−22−2000000002-2-2-22-2222-22-200-22-2002000000-2200000000−22−222−22−200000000
χ412-2-2-22-222-22-22002-2200-2000000-2200000000i2−i2−i2i2i2−i2−i2i2000000002-2-2-22-222-22-22002-2200-2000000-2200000000i2−i2−i2i2i2−i2−i2i200000000
χ422-2-2-22-222-22-22002-2200-2000000-2200000000−i2i2i2−i2−i2i2i2−i2000000002-2-2-22-222-22-22002-2200-2000000-2200000000−i2i2i2−i2−i2i2i2−i200000000
χ432-2-2-22-222-22-2200-22-20020000002-2000000002−2−22−222−2000000002-2-2-22-222-22-2200-22-20020000002-2000000002−2−22−222−200000000
χ442-2-2-22-222-22-2200-22-20020000002-200000000−222−22−2−22000000002-2-2-22-222-22-2200-22-20020000002-200000000−222−22−2−2200000000
χ4544-4-444-4-400004-4000-4400000000000000000000000000000000044-4-444-4-400004-4000-44000000000000000000000000000000000
χ4644-4-444-4-40000-440004-400000000000000000000000000000000044-4-444-4-40000-440004-4000000000000000000000000000000000
χ474-4444-4-4-4000000000000004-400000000000000000000000000004-4444-4-4-4000000000000004-40000000000000000000000000000
χ484-4444-4-4-400000000000000-4400000000000000000000000000004-4444-4-4-400000000000000-440000000000000000000000000000
χ494-44-4-44-444i−4i−4i4i00000000000000000000000000000000000000004-44-4-44-444i−4i−4i4i0000000000000000000000000000000000000000
χ504-44-4-44-44−4i4i4i−4i00000000000000000000000000000000000000004-44-4-44-44−4i4i4i−4i0000000000000000000000000000000000000000
χ514-4-44-444-40000004-4-4004000000000000000000000000000000004-4-44-444-40000004-4-400400000000000000000000000000000000
χ524-4-44-444-4000000-44400-4000000000000000000000000000000004-4-44-444-4000000-44400-400000000000000000000000000000000
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
χ57111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii
χ58111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i
χ59111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ60111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii
χ6111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-111-1-111-1-111
χ6211111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-111-1-111-1-1
χ6311111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-111-1-1
χ6411111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1-1-111-1-111
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
χ6922222222222222-2-2-222-2-2-2-2-222-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2222-2-222222-2-222000000000000000000000000
χ70222222222222-2-2222-2-22-2-2-2-2-2-222000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-222-2-2-222-2222222-2-2000000000000000000000000
χ7122222222-2-2-2-222-2-2-222-2-2-222-2-222000000000000000000000000-2-2-2-2-2-2-2-22222-2-2222-2-2222-2-222-2-2000000000000000000000000
χ7222222222-2-2-2-2-2-2222-2-22-2-22222-2-2000000000000000000000000-2-2-2-2-2-2-2-2222222-2-2-222-222-2-2-2-222000000000000000000000000
χ73222-2-2-22-200002222-2-2-2-22-2000000002-2002-20000000000000000-2-2-2222-220000-2-2-2-22222-2200000000-2200-220000000000000000
χ74222-2-2-22-200002222-2-2-2-22-200000000-2200-220000000000000000-2-2-2222-220000-2-2-2-22222-22000000002-2002-20000000000000000
χ75222-2-2-22-2000022-2-22-2-22-220000002i−2i002i−2i000000000000000000-2-2-2222-220000-2-222-222-22-2000000−2i2i00−2i2i000000000000000000
χ76222-2-2-22-2000022-2-22-2-22-22000000−2i2i00−2i2i000000000000000000-2-2-2222-220000-2-222-222-22-20000002i−2i002i−2i000000000000000000
χ77222-2-2-22-20000-2-222-222-2-220000002i−2i00−2i2i000000000000000000-2-2-2222-22000022-2-22-2-222-2000000−2i2i002i−2i000000000000000000
χ78222-2-2-22-20000-2-222-222-2-22000000−2i2i002i−2i000000000000000000-2-2-2222-22000022-2-22-2-222-20000002i−2i00−2i2i000000000000000000
χ79222-2-2-22-20000-2-2-2-222222-2000000002-200-220000000000000000-2-2-2222-2200002222-2-2-2-2-2200000000-22002-20000000000000000
χ80222-2-2-22-20000-2-2-2-222222-200000000-22002-20000000000000000-2-2-2222-2200002222-2-2-2-2-22000000002-200-220000000000000000
χ8122-22-2-2-222i2i−2i−2i2-20002-2000002i−2i0000000000000000002−2i2−i22−2i2−i2-2-22-2222-2−2i−2i2i2i-22000-2200000−2i2i000000000000000000−22−i2i2−22−i2i2
χ8222-22-2-2-222i2i−2i−2i2-20002-2000002i−2i000000000000000000−22−i2i2−22−i2i2-2-22-2222-2−2i−2i2i2i-22000-2200000−2i2i0000000000000000002−2i2−i22−2i2−i2
χ8322-22-2-2-222i2i−2i−2i-22000-2200000−2i2i000000000000000000i2−i2−22−i2i22−2-2-22-2222-2−2i−2i2i2i2-20002-2000002i−2i000000000000000000−i2i22−2i2−i2−22
χ8422-22-2-2-222i2i−2i−2i-22000-2200000−2i2i000000000000000000−i2i22−2i2−i2−22-2-22-2222-2−2i−2i2i2i2-20002-2000002i−2i000000000000000000i2−i2−22−i2i22−2
χ8522-22-2-2-22−2i−2i2i2i2-20002-200000−2i2i0000000000000000002−2−i2i22−2−i2i2-2-22-2222-22i2i−2i−2i-22000-22000002i−2i000000000000000000−22i2−i2−22i2−i2
χ8622-22-2-2-22−2i−2i2i2i2-20002-200000−2i2i000000000000000000−22i2−i2−22i2−i2-2-22-2222-22i2i−2i−2i-22000-22000002i−2i0000000000000000002−2−i2i22−2−i2i2
χ8722-22-2-2-22−2i−2i2i2i-22000-22000002i−2i000000000000000000i2−i22−2−i2i2−22-2-22-2222-22i2i−2i−2i2-20002-200000−2i2i000000000000000000−i2i2−22i2−i22−2
χ8822-22-2-2-22−2i−2i2i2i-22000-22000002i−2i000000000000000000−i2i2−22i2−i22−2-2-22-2222-22i2i−2i−2i2-20002-200000−2i2i000000000000000000i2−i22−2−i2i2−22
χ892-2-2-22-2222-22-2002-2200-20000002-200000000i2−i2i2−i2i2−i2i2−i200000000-2222-22-2-2-22-2200-22-2002000000-2200000000−i2i2−i2i2−i2i2−i2i200000000
χ902-2-2-22-2222-22-2002-2200-20000002-200000000−i2i2−i2i2−i2i2−i2i200000000-2222-22-2-2-22-2200-22-2002000000-2200000000i2−i2i2−i2i2−i2i2−i200000000
χ912-2-2-22-2222-22-200-22-2002000000-22000000002−22−2−22−2200000000-2222-22-2-2-22-22002-2200-20000002-200000000−22−222−22−200000000
χ922-2-2-22-2222-22-200-22-2002000000-2200000000−22−222−22−200000000-2222-22-2-2-22-22002-2200-20000002-2000000002−22−2−22−2200000000
χ932-2-2-22-222-22-22002-2200-2000000-2200000000i2−i2−i2i2i2−i2−i2i200000000-2222-22-2-22-22-200-22-20020000002-200000000−i2i2i2−i2−i2i2i2−i200000000
χ942-2-2-22-222-22-22002-2200-2000000-2200000000−i2i2i2−i2−i2i2i2−i200000000-2222-22-2-22-22-200-22-20020000002-200000000i2−i2−i2i2i2−i2−i2i200000000
χ952-2-2-22-222-22-2200-22-20020000002-2000000002−2−22−222−200000000-2222-22-2-22-22-2002-2200-2000000-2200000000−222−22−2−2200000000
χ962-2-2-22-222-22-2200-22-20020000002-200000000−222−22−2−2200000000-2222-22-2-22-22-2002-2200-2000000-22000000002−2−22−222−200000000
χ9744-4-444-4-400004-4000-44000000000000000000000000000000000-4-444-4-4440000-440004-4000000000000000000000000000000000
χ9844-4-444-4-40000-440004-4000000000000000000000000000000000-4-444-4-44400004-4000-44000000000000000000000000000000000
χ994-4444-4-4-4000000000000004-40000000000000000000000000000-44-4-4-444400000000000000-440000000000000000000000000000
χ1004-4444-4-4-400000000000000-440000000000000000000000000000-44-4-4-4444000000000000004-40000000000000000000000000000
χ1014-44-4-44-444i−4i−4i4i0000000000000000000000000000000000000000-44-444-44-4−4i4i4i−4i0000000000000000000000000000000000000000
χ1024-44-4-44-44−4i4i4i−4i0000000000000000000000000000000000000000-44-444-44-44i−4i−4i4i0000000000000000000000000000000000000000
χ1034-4-44-444-40000004-4-400400000000000000000000000000000000-444-44-4-44000000-44400-400000000000000000000000000000000
χ1044-4-44-444-4000000-44400-400000000000000000000000000000000-444-44-4-440000004-4-400400000000000000000000000000000000

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