Finite Group Databasebeta

← Group #10693078

Character table — Group #10693078

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order1222223444444666121212124446612121212121222446666888812121212121224242424242424248824242424244488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-111-1-11111ii−i−i1-1-1-1-1-1iiii−i−i−i−ii−iii−i−i1-1-11ii−i−i1-1i−i
χ101111111-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-111-1-11111ii−i−i1-1-1-1-1-1iiii−i−i−i−ii−iii−i−i-111-1−i−iii-11−ii
χ111111111-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-111-1-11111−i−iii1-1-1-1-1-1−i−i−i−iiiii−ii−i−iii1-1-11−i−iii1-1−ii
χ121111111-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-111-1-11111−i−iii1-1-1-1-1-1−i−i−i−iiiii−ii−i−iii-111-1ii−i−i-11i−i
χ131111111-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-1-1-111-1-1-1-1ii−i−i1-11111iiii−i−i−i−i−ii−i−iii1-1-11ii−i−i-11−ii
χ141111111-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-1-1-111-1-1-1-1ii−i−i1-11111iiii−i−i−i−i−ii−i−iii-111-1−i−iii1-1i−i
χ151111111-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-1-1-111-1-1-1-1−i−iii1-11111−i−i−i−iiiiii−iii−i−i1-1-11−i−iii-11i−i
χ161111111-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-1-1-111-1-1-1-1−i−iii1-11111−i−i−i−iiiiii−iii−i−i-111-1ii−i−i1-1−ii
χ1722222222222-2-22222222-2-2-222-2-222-2-2000000000000-2-200000000000000000022-2-200000000
χ1822222222222-2-22222222-2-2-222-2-222-2-2000000000000-2-2000000000000000000-2-22200000000
χ192222222-2-2-2-222222-2-2-2-2-2-2222-2-2-2-222000000000000-220000000000000000002-22-200000000
χ202222222-2-2-2-222222-2-2-2-2-2-2222-2-2-2-222000000000000-22000000000000000000-22-2200000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-111111111111122-1-1-1-1000000000000
χ25222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1-1-1111122-2-2-1-1-1-12i2i−2i−2i-111111−i−i−i−iiiii2i−2i−i−iii000000000000
χ26222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1-1-1111122-2-2-1-1-1-1−2i−2i2i2i-111111iiii−i−i−i−i−2i2iii−i−i000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1-1-11111-2-22211112i2i−2i−2i-11-1-1-1-1−i−i−i−iiiii−2i2iii−i−i000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1-1-11111-2-2221111−2i−2i2i2i-11-1-1-1-1iiii−i−i−i−i2i−2i−i−iii000000000000
χ292222-2-2222-2-22222222222-2-2-2-222-2-222000000002-22-2-2-2000022-2-222-2-2000000000000000000
χ302222-2-2222-2-22222222222-2-2-2-222-2-22200000000-22-22-2-20000-2-222-2-222000000000000000000
χ312222-2-2222-2-2-2-22222222-222-2-2-2-2-2-2-2-20000000000002200000000000000000000002i−2i2i−2i0000
χ322222-2-2222-2-2-2-22222222-222-2-2-2-2-2-2-2-2000000000000220000000000000000000000−2i2i−2i2i0000
χ332222-2-22-2-22222222-2-2-2-2-22-2-2-2-2-222220000000000002-200000000000000000000002-2-220000
χ342222-2-22-2-22222222-2-2-2-2-22-2-2-2-2-222220000000000002-20000000000000000000000-222-20000
χ352222-2-22-2-222-2-2222-2-2-2-22-22-2-22222-2-2000000002i−2i−2i2i-2200002i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-2-222-2-2222-2-2-2-22-22-2-22222-2-200000000−2i2i2i−2i-220000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-122-2-222-1-1-1-1-1-1-12-2-211-1-111-1-10000−i3−i3i3i32-22-211−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ382222-2-2-122-2-222-1-1-1-1-1-1-12-2-211-1-111-1-10000−i3−i3i3i3-22-2211−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ392222-2-2-122-2-222-1-1-1-1-1-1-12-2-211-1-111-1-10000i3i3−i3−i32-22-211i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ402222-2-2-122-2-222-1-1-1-1-1-1-12-2-211-1-111-1-10000i3i3−i3−i3-22-2211i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ412222-2-2-1-2-222-2-2-1-1-111112-2211-1-1-1-1110000−i3−i3i3i32i−2i−2i2i1-1i3i3−i3−i3−i−iiiii−i−i003−3−33000000000000
χ422222-2-2-1-2-222-2-2-1-1-111112-2211-1-1-1-1110000−i3−i3i3i3−2i2i2i−2i1-1i3i3−i3−i3ii−i−i−i−iii00−333−3000000000000
χ432222-2-2-1-2-222-2-2-1-1-111112-2211-1-1-1-1110000i3i3−i3−i32i−2i−2i2i1-1−i3−i3i3i3−i−iiiii−i−i00−333−3000000000000
χ442222-2-2-1-2-222-2-2-1-1-111112-2211-1-1-1-1110000i3i3−i3−i3−2i2i2i−2i1-1−i3−i3i3i3ii−i−i−i−iii003−3−33000000000000
χ45444444-24444-4-4-2-2-2-2-2-2-2-4-4-4-2-222-2-22200000000000022000000000000000000000000000000
χ46444444-2-4-4-4-444-2-2-22222-4-44-2-22222-2-20000000000002-2000000000000000000000000000000
χ474444-4-4-244-4-4-4-4-2-2-2-2-2-2-2-44422222222000000000000-2-2000000000000000000000000000000
χ484444-4-4-2-4-44444-2-2-22222-44-42222-2-2-2-2000000000000-22000000000000000000000000000000
χ4944-4-400400004i−4i4-4-400000000000004i−4i2-22i−2i2-22-20000002i−2i2i−2i00000000000000000000000000
χ5044-4-400400004i−4i4-4-400000000000004i−4i-22−2i2i-22-22000000−2i2i−2i2i00000000000000000000000000
χ5144-4-40040000−4i4i4-4-40000000000000−4i4i2-2−2i2i2-22-2000000−2i2i−2i2i00000000000000000000000000
χ5244-4-40040000−4i4i4-4-40000000000000−4i4i-222i−2i-22-220000002i−2i2i−2i00000000000000000000000000
χ5344-4-400-200004i−4i-2222323−23−2300000−2i32i300−2i2i2-22i−2i−1−i31+i3−1+i31−i30000002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ5444-4-400-200004i−4i-2222323−23−2300000−2i32i300−2i2i-22−2i2i1+i3−1−i31−i3−1+i3000000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ5544-4-400-200004i−4i-222−23−232323000002i3−2i300−2i2i2-22i−2i−1+i31−i3−1−i31+i30000002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ5644-4-400-200004i−4i-222−23−232323000002i3−2i300−2i2i-22−2i2i1−i3−1+i31+i3−1−i3000000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ5744-4-400-20000−4i4i-2222323−23−23000002i3−2i3002i−2i2-2−2i2i−1+i31−i3−1−i31+i3000000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ5844-4-400-20000−4i4i-2222323−23−23000002i3−2i3002i−2i-222i−2i1−i3−1+i31+i3−1−i30000002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ5944-4-400-20000−4i4i-222−23−23232300000−2i32i3002i−2i2-2−2i2i−1−i31+i3−1+i31−i3000000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ6044-4-400-20000−4i4i-222−23−23232300000−2i32i3002i−2i-222i−2i1+i3−1−i31−i3−1+i30000002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ614-44-44-444i−4i4i−4i00-44-44i−4i4i−4i0004-4004i−4i0000000000000000000000000000000000000000000000
χ624-44-44-44−4i4i−4i4i00-44-4−4i4i−4i4i0004-400−4i4i0000000000000000000000000000000000000000000000
χ634-44-44-4-24i−4i4i−4i002-22−2i2i−2i2i000-2200−2i2i00000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000
χ644-44-44-4-24i−4i4i−4i002-22−2i2i−2i2i000-2200−2i2i00000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000
χ654-44-44-4-2−4i4i−4i4i002-222i−2i2i−2i000-22002i−2i00000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000
χ664-44-44-4-2−4i4i−4i4i002-222i−2i2i−2i000-22002i−2i00000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000
χ674-44-4-4444i−4i−4i4i00-44-44i−4i4i−4i000-4400−4i4i0000000000000000000000000000000000000000000000
χ684-44-4-444−4i4i4i−4i00-44-4−4i4i−4i4i000-44004i−4i0000000000000000000000000000000000000000000000
χ694-44-4-44-24i−4i−4i4i002-22−2i2i−2i2i0002-2002i−2i00000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000
χ704-44-4-44-24i−4i−4i4i002-22−2i2i−2i2i0002-2002i−2i00000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000
χ714-44-4-44-2−4i4i4i−4i002-222i−2i2i−2i0002-200−2i2i00000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000
χ724-44-4-44-2−4i4i4i−4i002-222i−2i2i−2i0002-200−2i2i00000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000
χ738-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000
χ758-8-8800-400000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000

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