Finite Group Databasebeta

← Group #10692521

Character table — Group #10692521

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222234444446661212121244466888888881212121212124444121212121212121212122424242424242424224444448888888888242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-111-1-11-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−i1-1i−i
χ101111111-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-111-1-11-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiii−iii−i−i-11−ii
χ111111111-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−ii−i−iii-11−ii
χ121111111-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ii−i−iii1-1i−i
χ131111111-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-111-1-11-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii1-1−ii
χ141111111-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-111-1-11-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−ii−i−iii-11i−i
χ151111111-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiii−iii−i−i-11i−i
χ161111111-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−ii−iii−i−i1-1−ii
χ1722222222222-2-22222222-2-2-22200000000-2-222-2-20000-2-2000000000000000022-2-2-2-222000000000000000000
χ1822222222222-2-22222222-2-2-22200000000-2-222-2-20000-2-20000000000000000-2-22222-2-2000000000000000000
χ192222222-2-2-2-222222-2-2-2-22-2-22200000000-2-2-2-2220000-22000000000000000022-2-222-2-2000000000000000000
χ202222222-2-2-2-222222-2-2-2-22-2-22200000000-2-2-2-2220000-220000000000000000-2-222-2-222000000000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ25222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i2i2i−2i−2i−2i−2i-1-1111122-2-2-11-1-1-1-11111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ26222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i2i2i−2i−2i−2i−2i-1-11111-2-222-111111-1-1-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i−2i−2i2i2i2i2i-1-1111122-2-2-11-1-1-1-11111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i−2i−2i2i2i2i2i-1-11111-2-222-111111-1-1-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ292222-2-2222-2-2222222222-22-2-2-20000000022-2-2220000-2-200000000000000000000000022-2-222-2-20000000000
χ302222-2-2222-2-2222222222-22-2-2-20000000022-2-2220000-2-2000000000000000000000000-2-222-2-2220000000000
χ312222-2-2222-2-2-2-222222222-22-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-2000022000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ322222-2-2222-2-2-2-222222222-22-2-2−2i−2i2i2i−2i−2i2i2i-2-2-2-2-2-200002200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ332222-2-22-2-22222222-2-2-2-2-2-22-2-222-2-2-2-222-2-2222200002-20000000022-2-2-2-22200000000000000000000000000
χ342222-2-22-2-22222222-2-2-2-2-2-22-2-2-2-22222-2-2-2-2222200002-200000000-2-22222-2-200000000000000000000000000
χ352222-2-22-2-222-2-2222-2-2-2-222-2-2-2000000002222-2-20000-220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ362222-2-22-2-222-2-2222-2-2-2-222-2-2-2000000002222-2-20000-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ372222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-22112i2i−2i−2i2i2i−2i−2i1111110000-1-133−3−333−3−3−i−iii−i−iii000000000000000000−i3i3−i3i30000
χ382222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-22112i2i−2i−2i2i2i−2i−2i1111110000-1-1−3−333−3−333−i−iii−i−iii000000000000000000i3−i3i3−i30000
χ392222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-2211−2i−2i2i2i−2i−2i2i2i1111110000-1-133−3−333−3−3ii−i−iii−i−i000000000000000000i3−i3i3−i30000
χ402222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-2211−2i−2i2i2i−2i−2i2i2i1111110000-1-1−3−333−3−333ii−i−iii−i−i000000000000000000−i3i3−i3i30000
χ412222-2-2-1-2-22222-1-1-11111-2-221122-2-2-2-22211-1-1-1-10000-1133−3−3−3−333-1-11111-1-1000000000000000000−333−30000
χ422222-2-2-1-2-22222-1-1-11111-2-221122-2-2-2-22211-1-1-1-10000-11−3−33333−3−3-1-11111-1-10000000000000000003−3−330000
χ432222-2-2-1-2-22222-1-1-11111-2-2211-2-22222-2-211-1-1-1-10000-1133−3−3−3−33311-1-1-1-1110000000000000000003−3−330000
χ442222-2-2-1-2-22222-1-1-11111-2-2211-2-22222-2-211-1-1-1-10000-11−3−33333−3−311-1-1-1-111000000000000000000−333−30000
χ4522-2-22-222i−2i2i−2i002-2-22i2i−2i−2i0002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ4622-2-22-222i−2i2i−2i002-2-22i2i−2i−2i0002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i-220000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ4722-2-22-222i−2i2i−2i002-2-22i2i−2i−2i0002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ4822-2-22-222i−2i2i−2i002-2-22i2i−2i−2i0002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i-220000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ4922-2-22-22−2i2i−2i2i002-2-2−2i−2i2i2i0002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ5022-2-22-22−2i2i−2i2i002-2-2−2i−2i2i2i0002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i-2200002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ5122-2-22-22−2i2i−2i2i002-2-2−2i−2i2i2i0002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ5222-2-22-22−2i2i−2i2i002-2-2−2i−2i2i2i0002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i-2200002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ5322-2-2-2222i−2i−2i2i002-2-22i2i−2i−2i000-221−i−1+i−1+i1−i−1−i1+i1+i−1−i00−2i2i00000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i002i−2i2-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ5422-2-2-2222i−2i−2i2i002-2-22i2i−2i−2i000-221−i−1+i−1+i1−i−1−i1+i1+i−1−i00−2i2i00000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00−2i2i-2200−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ5522-2-2-2222i−2i−2i2i002-2-22i2i−2i−2i000-22−1+i1−i1−i−1+i1+i−1−i−1−i1+i00−2i2i0000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i002i−2i2-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ5622-2-2-2222i−2i−2i2i002-2-22i2i−2i−2i000-22−1+i1−i1−i−1+i1+i−1−i−1−i1+i00−2i2i0000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00−2i2i-22001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ5722-2-2-222−2i2i2i−2i002-2-2−2i−2i2i2i000-221+i−1−i−1−i1+i−1+i1−i1−i−1+i002i−2i00000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i002i−2i-2200−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ5822-2-2-222−2i2i2i−2i002-2-2−2i−2i2i2i000-221+i−1−i−1−i1+i−1+i1−i1−i−1+i002i−2i00000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00−2i2i2-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ5922-2-2-222−2i2i2i−2i002-2-2−2i−2i2i2i000-22−1−i1+i1+i−1−i1−i−1+i−1+i1−i002i−2i0000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i002i−2i-22001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ6022-2-2-222−2i2i2i−2i002-2-2−2i−2i2i2i000-22−1−i1+i1+i−1−i1−i−1+i−1+i1−i002i−2i0000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00−2i2i2-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ61444444-24444-4-4-2-2-2-2-2-2-2-4-4-4-2-20000000022-2-222000022000000000000000000000000000000000000000000
χ62444444-2-4-4-4-444-2-2-222224-4-4-2-2000000002222-2-200002-2000000000000000000000000000000000000000000
χ634444-4-4-244-4-444-2-2-2-2-2-2-2-44-42200000000-2-222-2-2000022000000000000000000000000000000000000000000
χ644444-4-4-2-4-444-4-4-2-2-2222244-42200000000-2-2-2-22200002-2000000000000000000000000000000000000000000
χ6544-4-44-4-24i−4i4i−4i00-222−2i−2i2i2i000-222+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00−2i2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000
χ6644-4-44-4-24i−4i4i−4i00-222−2i−2i2i2i000-22−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00−2i2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000
χ6744-4-44-4-2−4i4i−4i4i00-2222i2i−2i−2i000-222−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i002i−2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000
χ6844-4-44-4-2−4i4i−4i4i00-2222i2i−2i−2i000-22−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i002i−2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000
χ6944-4-4-44-24i−4i−4i4i00-222−2i−2i2i2i0002-22−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i002i−2i0000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000000000000000
χ7044-4-4-44-24i−4i−4i4i00-222−2i−2i2i2i0002-2−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i002i−2i00000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000000000000000
χ7144-4-4-44-2−4i4i4i−4i00-2222i2i−2i−2i0002-22+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00−2i2i0000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000000000000000
χ7244-4-4-44-2−4i4i4i−4i00-2222i2i−2i−2i0002-2−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00−2i2i00000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000000000000000
χ734-44-400400004i−4i-44-40000000000000000000004i−4i2-22i−2i002-22-22i−2i2i−2i0000000000000000000000000000000000
χ744-44-400400004i−4i-44-40000000000000000000004i−4i-22−2i2i00-22-22−2i2i−2i2i0000000000000000000000000000000000
χ754-44-40040000−4i4i-44-4000000000000000000000−4i4i2-2−2i2i002-22-2−2i2i−2i2i0000000000000000000000000000000000
χ764-44-40040000−4i4i-44-4000000000000000000000−4i4i-222i−2i00-22-222i−2i2i−2i0000000000000000000000000000000000
χ774-44-400-200004i−4i2-22−2i32i3−2i32i3000000000000023−2300−2i2i2-22i−2i00−1+31−3−1−31+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000000000000000
χ784-44-400-200004i−4i2-22−2i32i3−2i32i3000000000000023−2300−2i2i-22−2i2i001−3−1+31+3−1−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000000000000000
χ794-44-400-200004i−4i2-222i3−2i32i3−2i30000000000000−232300−2i2i2-22i−2i00−1−31+3−1+31−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000000000000000
χ804-44-400-200004i−4i2-222i3−2i32i3−2i30000000000000−232300−2i2i-22−2i2i001+3−1−31−3−1+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000000000000000
χ814-44-400-20000−4i4i2-22−2i32i3−2i32i30000000000000−2323002i−2i2-2−2i2i00−1−31+3−1+31−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000000000000000
χ824-44-400-20000−4i4i2-22−2i32i3−2i32i30000000000000−2323002i−2i-222i−2i001+3−1−31−3−1+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000000000000000
χ834-44-400-20000−4i4i2-222i3−2i32i3−2i3000000000000023−23002i−2i2-2−2i2i00−1+31−3−1−31+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000000000000000
χ844-44-400-20000−4i4i2-222i3−2i32i3−2i3000000000000023−23002i−2i-222i−2i001−3−1+31+3−1−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000000000000000
χ858-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.