Finite Group Databasebeta

← Group #10765652

Character table — Group #10765652

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111111122222222222244444444444444444444444444444444444444448888888812121212121212121616161616161616242424242424242424242424
order122244443444466612121212888888888888121212122424242424242424242424242424242424242424242424242444888824448888612121224242424244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-1-111-1-111-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111
χ911111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1
χ171111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i11-1-1ii−i−i1-11-1i−ii−i1-11-1i−ii−i1-1i−i
χ181111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i-1-111−i−iii1-11-1i−ii−i-11-11−ii−ii-11−ii
χ191111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii11-1-1ii−i−i-11-11−ii−ii-11-11−ii−ii1-1i−i
χ201111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii-1-111−i−iii-11-11−ii−ii1-11-1i−ii−i-11−ii
χ211111-1-1-1-1111-1-1111-1-1-1-1ii−i−i-1-111−i−iii11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii11-1-1ii−i−i1-1-11i−i−ii1-1-11i−i−ii-11−ii
χ221111-1-1-1-1111-1-1111-1-1-1-1ii−i−i-1-111−i−iii11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii-1-111−i−iii1-1-11i−i−ii-111-1−iii−i1-1i−i
χ231111-1-1-1-1111-1-1111-1-1-1-1ii−i−i-1-111−i−iii11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-111-1−iii−i11-1-1ii−i−i-111-1−iii−i-111-1−iii−i-11−ii
χ241111-1-1-1-1111-1-1111-1-1-1-1ii−i−i-1-111−i−iii11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-111-1−iii−i-1-111−i−iii-111-1−iii−i1-1-11i−i−ii1-1i−i
χ251111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii11-1-1−i−iii1-11-1−ii−ii1-11-1−ii−ii1-1−ii
χ261111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii-1-111ii−i−i1-11-1−ii−ii-11-11i−ii−i-11i−i
χ271111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i11-1-1−i−iii-11-11i−ii−i-11-11i−ii−i1-1−ii
χ281111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i-1-111ii−i−i-11-11i−ii−i1-11-1−ii−ii-11i−i
χ291111-1-1-1-1111-1-1111-1-1-1-1−i−iii-1-111ii−i−i11-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i11-1-1−i−iii1-1-11−iii−i1-1-11−iii−i-11i−i
χ301111-1-1-1-1111-1-1111-1-1-1-1−i−iii-1-111ii−i−i11-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i-1-111ii−i−i1-1-11−iii−i-111-1i−i−ii1-1−ii
χ311111-1-1-1-1111-1-1111-1-1-1-1−i−iii-1-111ii−i−i11-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii11-1-1−i−iii-111-1i−i−ii-111-1i−i−ii-11i−i
χ321111-1-1-1-1111-1-1111-1-1-1-1−i−iii-1-111ii−i−i11-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii-1-111ii−i−i-111-1i−i−ii1-1-11−iii−i1-1−ii
χ33222222222-2-2-2-222222222-22-200000000-2-2-2-222-2-222-2-20000000000000000000000002-22-22-22-200000000000000000000
χ34222222222-2-2-2-222222222-22-200000000-2-2-2-222-2-222-2-2000000000000000000000000-22-22-22-2200000000000000000000
χ35222222222-2-2-2-22222222-22-2200000000-2-2-2-2-2-222-2-2220000000000000000000000002-22-2-22-2200000000000000000000
χ36222222222-2-2-2-22222222-22-2200000000-2-2-2-2-2-222-2-222000000000000000000000000-22-222-22-200000000000000000000
χ3722222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222200000000-1-1-1-1-1-1-1-1000000000000
χ3822222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-20000000011111111000000000000
χ3922222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-222-2-200000000-1-111-1-111000000000000
χ4022222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-222-2-2220000000011-1-111-1-1000000000000
χ4122222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111112222-2-2-2-200000000-1-1-1-11111000000000000
χ4222222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-2-2-22222000000001111-1-1-1-1000000000000
χ4322222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-122-2-2-2-22200000000-1-11111-1-1000000000000
χ4422222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-2-22222-2-20000000011-1-1-1-111000000000000
χ452222-2-2-2-22-2-222222-2-2-2-22i−2i−2i2i00000000-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000002-2-222i−2i−2i2i00000000000000000000
χ462222-2-2-2-22-2-222222-2-2-2-22i−2i−2i2i00000000-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000-222-2−2i2i2i−2i00000000000000000000
χ472222-2-2-2-22-2-222222-2-2-2-2−2i2i2i−2i00000000-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-2-22−2i2i2i−2i00000000000000000000
χ482222-2-2-2-22-2-222222-2-2-2-2−2i2i2i−2i00000000-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000-222-22i−2i−2i2i00000000000000000000
χ492222-2-2-2-2-122-2-2-1-1-111112i2i−2i−2i22-2-22i2i−2i−2i-1-111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii2-22-22i−2i2i−2i00000000-11-11−ii−ii000000000000
χ502222-2-2-2-2-122-2-2-1-1-111112i2i−2i−2i22-2-22i2i−2i−2i-1-111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-22-22−2i2i−2i2i000000001-11-1i−ii−i000000000000
χ512222-2-2-2-2-122-2-2-1-1-111112i2i−2i−2i-2-222−2i−2i2i2i-1-111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i2-2-222i−2i−2i2i00000000-111-1−iii−i000000000000
χ522222-2-2-2-2-122-2-2-1-1-111112i2i−2i−2i-2-222−2i−2i2i2i-1-111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-222-2−2i2i2i−2i000000001-1-11i−i−ii000000000000
χ532222-2-2-2-2-122-2-2-1-1-11111−2i−2i2i2i22-2-2−2i−2i2i2i-1-111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i2-22-2−2i2i−2i2i00000000-11-11i−ii−i000000000000
χ542222-2-2-2-2-122-2-2-1-1-11111−2i−2i2i2i22-2-2−2i−2i2i2i-1-111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-22-222i−2i2i−2i000000001-11-1−ii−ii000000000000
χ552222-2-2-2-2-122-2-2-1-1-11111−2i−2i2i2i-2-2222i2i−2i−2i-1-111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii2-2-22−2i2i2i−2i00000000-111-1i−i−ii000000000000
χ562222-2-2-2-2-122-2-2-1-1-11111−2i−2i2i2i-2-2222i2i−2i−2i-1-111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-222-22i−2i−2i2i000000001-1-11−iii−i000000000000
χ5744444444-2-4-4-4-4-2-2-2-2-2-2-24-44-4000000002222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ5844444444-2-4-4-4-4-2-2-2-2-2-2-2-44-4400000000222222-2-222-2-20000000000000000000000000000000000000000000000000000
χ594444-4-4-4-4-2-4-444-2-2-222224i−4i−4i4i0000000022-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ604444-4-4-4-4-2-4-444-2-2-22222−4i4i4i−4i0000000022-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ6144-4-444-4-4400004-4-444-4-40000−2i22i2−2i22i20000000000000000−2i2−2i22i22i2−2i2−2i22i22i200000000000000000000000000000000000000000000
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χ6344-4-444-4-4-20000-222-2-2220000−2i22i2−2i22i200000000−2i32i300−2i32i300i2i2−i2−i2i2i2−i2−i266−6−666−6−6000000000000000000000000000000000000
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χ7144-4-4-4-444-20000-22222-2-200002i2−2i2−2i22i20000000023−2300−232300−i2−i2i2i2i2i2−i2−i2−i6−i6i6i6i6i6−i6−i6000000000000000000000000000000000000
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χ744-44-44i−4i4i−4i40000-44-44i−4i4i−4i00000000−2−2i2+2i−2+2i2−2i00000000000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000000000000000000000000000000000
χ754-44-44i−4i4i−4i-200002-22−2i2i−2i2i000000002+2i−2−2i2−2i−2+2i0000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ236−66−6i6−i6i6−i6−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000000000000000
χ764-44-44i−4i4i−4i-200002-22−2i2i−2i2i000000002+2i−2−2i2−2i−2+2i000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23−66−66−i6i6−i6i6−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000000000000000
χ774-44-44i−4i4i−4i-200002-22−2i2i−2i2i00000000−2−2i2+2i−2+2i2−2i0000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ23−66−66−i6i6−i6i61+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000000000000000
χ784-44-44i−4i4i−4i-200002-22−2i2i−2i2i00000000−2−2i2+2i−2+2i2−2i000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ236−66−6i6−i6i6−i61+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000000000000000
χ794-44-4−4i4i−4i4i40000-44-4−4i4i−4i4i000000002−2i−2+2i2+2i−2−2i000000000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000000000000000000000000000000000000
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χ814-44-4−4i4i−4i4i-200002-222i−2i2i−2i000000002−2i−2+2i2+2i−2−2i000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ136−66−6−i6i6−i6i6−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000000000000000
χ824-44-4−4i4i−4i4i-200002-222i−2i2i−2i000000002−2i−2+2i2+2i−2−2i0000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13−66−66i6−i6i6−i6−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i-200002-222i−2i2i−2i00000000−2+2i2−2i−2−2i2+2i000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13−66−66i6−i6i6−i61−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i-200002-222i−2i2i−2i00000000−2+2i2−2i−2−2i2+2i0000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ136−66−6−i6i6−i6i61−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000000000000000
χ854-4-444i−4i−4i4i44-44i−4i-4-444i−4i−4i4i0000000000004-44i−4i000000000000000000000000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i4-44−4i4i-4-444i−4i−4i4i000000000000-44−4i4i000000000000000000000000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i-24-44i−4i22-2−2i2i2i−2i000000000000-22−2i2i00000000−2i32i32i3−2i323−23−232300000000000000000000000000000000000000000000
χ884-4-444i−4i−4i4i-24-44i−4i22-2−2i2i2i−2i000000000000-22−2i2i000000002i3−2i3−2i32i3−232323−2300000000000000000000000000000000000000000000
χ894-4-444i−4i−4i4i-2-44−4i4i22-2−2i2i2i−2i0000000000002-22i−2i00000000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ13−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000000000
χ904-4-444i−4i−4i4i-2-44−4i4i22-2−2i2i2i−2i0000000000002-22i−2i0000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i44-4−4i4i-4-44−4i4i4i−4i0000000000004-4−4i4i000000000000000000000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i4-444i−4i-4-44−4i4i4i−4i000000000000-444i−4i000000000000000000000000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i-24-4−4i4i22-22i−2i−2i2i000000000000-222i−2i00000000−2i32i32i3−2i3−232323−2300000000000000000000000000000000000000000000
χ944-4-44−4i4i4i−4i-24-4−4i4i22-22i−2i−2i2i000000000000-222i−2i000000002i3−2i3−2i32i323−23−232300000000000000000000000000000000000000000000
χ954-4-44−4i4i4i−4i-2-444i−4i22-22i−2i−2i2i0000000000002-2−2i2i0000000000000000−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ964-4-44−4i4i4i−4i-2-444i−4i22-22i−2i−2i2i0000000000002-2−2i2i00000000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.