Finite Group Databasebeta

← Group #10695213

Character table — Group #10695213

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222224444444434444444466666661212121212121212444444441212121212121212121212121212121212121212121212128888888824242424242424242424242424242424888888888888888844444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-2222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ252222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ262222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ3022222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ3122222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ3222222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
χ3322222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−333000000000000000000000000
χ3422222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−3000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−3000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−333000000000000000000000000
χ372222-2-2-2-22222-2-2-2-2222-2-222-2-2222-2-2-2-22222-2-2-2-20000000022-2-222-2-200000000000000000000000000000000000000000000000022-2-222-2-200000000
χ382222-2-2-2-22222-2-2-2-2222-2-222-2-2222-2-2-2-22222-2-2-2-20000000022-2-222-2-2000000000000000000000000000000000000000000000000-2-222-2-22200000000
χ392222-2-2-2-22222-2-2-2-22-2-222-2-222222-2-2-2-22222-2-2-2-200000000-2-222-2-222000000000000000000000000000000000000000022-2-222-2-20000000000000000
χ402222-2-2-2-22222-2-2-2-22-2-222-2-222222-2-2-2-22222-2-2-2-200000000-2-222-2-2220000000000000000000000000000000000000000-2-222-2-2220000000000000000
χ412222-2-2-2-2-2-2-2-22222222-2-2-2-222222-2-2-2-2-2-2-2-222220000000022-2-2-2-2220000000000000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ422222-2-2-2-2-2-2-2-22222222-2-2-2-222222-2-2-2-2-2-2-2-222220000000022-2-2-2-222000000000000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ432222-2-2-2-2-2-2-2-222222-2-22222-2-2222-2-2-2-2-2-2-2-2222200000000-2-22222-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ442222-2-2-2-2-2-2-2-222222-2-22222-2-2222-2-2-2-2-2-2-2-2222200000000-2-22222-2-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ4522-2-222-2-222-2-222-2-22000000002-2-222-2-222-2-222-2-2002i−2i002i−2i0000000000002i2i−2i−2i00002i2i−2i−2i0000000000000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ4622-2-222-2-222-2-222-2-22000000002-2-222-2-222-2-222-2-2002i−2i002i−2i0000000000002i2i−2i−2i00002i2i−2i−2i000000000000000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ4722-2-222-2-222-2-222-2-22000000002-2-222-2-222-2-222-2-200−2i2i00−2i2i000000000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ4822-2-222-2-222-2-222-2-22000000002-2-222-2-222-2-222-2-200−2i2i00−2i2i000000000000−2i−2i2i2i0000−2i−2i2i2i000000000000000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ4922-2-222-2-2-2-222-2-2222000000002-2-222-2-2-2-222-2-222002i−2i00−2i2i0000000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ5022-2-222-2-2-2-222-2-2222000000002-2-222-2-2-2-222-2-222002i−2i00−2i2i0000000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ5122-2-222-2-2-2-222-2-2222000000002-2-222-2-2-2-222-2-22200−2i2i002i−2i000000000000−2i−2i2i2i00002i2i−2i−2i000000000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ5222-2-222-2-2-2-222-2-2222000000002-2-222-2-2-2-222-2-22200−2i2i002i−2i000000000000−2i−2i2i2i00002i2i−2i−2i000000000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ5322-2-2-2-22222-2-2-2-2222000000002-2-2-2-22222-2-2-2-2222i−2i002i−2i00000000002i2i−2i−2i00002i2i−2i−2i00000000000000000000000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000
χ5422-2-2-2-22222-2-2-2-2222000000002-2-2-2-22222-2-2-2-2222i−2i002i−2i00000000002i2i−2i−2i00002i2i−2i−2i0000000000000000000000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000
χ5522-2-2-2-22222-2-2-2-2222000000002-2-2-2-22222-2-2-2-222−2i2i00−2i2i0000000000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000
χ5622-2-2-2-22222-2-2-2-2222000000002-2-2-2-22222-2-2-2-222−2i2i00−2i2i0000000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000
χ5722-2-2-2-222-2-22222-2-22000000002-2-2-2-222-2-22222-2-22i−2i00−2i2i00000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−2200000000
χ5822-2-2-2-222-2-22222-2-22000000002-2-2-2-222-2-22222-2-22i−2i00−2i2i00000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000i2−i2−i2i2−i2i2i2−i22−2−22−222−200000000
χ5922-2-2-2-222-2-22222-2-22000000002-2-2-2-222-2-22222-2-2−2i2i002i−2i0000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000−i2i2i2−i2i2−i2−i2i22−2−22−222−200000000
χ6022-2-2-2-222-2-22222-2-22000000002-2-2-2-222-2-22222-2-2−2i2i002i−2i0000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−2200000000
χ612-22-22-22-22i−2i2i−2i2i−2i2i−2i22-22-22i−2i2i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i0000000000000000000000000000000000000000000000000000000000002i−2i2-2
χ622-22-22-22-22i−2i2i−2i2i−2i2i−2i22-22-22i−2i2i−2i-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i000000000000000000000000000000000000000000000000000000000000−2i2i-22
χ632-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22-22−2i2i−2i2i-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i000000000000000000000000000000000000000000000000000000002i−2i2-20000
χ642-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22-22−2i2i−2i2i-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i00000000000000000000000000000000000000000000000000000000−2i2i-220000
χ652-22-22-22-2−2i2i−2i2i−2i2i−2i2i22-22-2−2i2i−2i2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000002i−2i-22
χ662-22-22-22-2−2i2i−2i2i−2i2i−2i2i22-22-2−2i2i−2i2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000−2i2i2-2
χ672-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-222i−2i2i−2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i000000000000000000000000000000000000000000000000000000002i−2i-220000
χ682-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-22-222i−2i2i−2i-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i00000000000000000000000000000000000000000000000000000000−2i2i2-20000
χ692-22-2-22-222i−2i2i−2i−2i2i−2i2i22-2-222i−2i−2i2i-22-2-22-222i−2i2i−2i−2i2i−2i2i000000002-2-222i−2i−2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ702-22-2-22-222i−2i2i−2i−2i2i−2i2i22-2-222i−2i−2i2i-22-2-22-222i−2i2i−2i−2i2i−2i2i000000002-2-222i−2i−2i2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.