Finite Group Databasebeta

← Group #10691492

Character table — Group #10691492

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order1222223444444666121212122222444666612121212244444666661212121212121212121212121288888824242424888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111-1-111-1-111111111-1-111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111-1-111-1-111111111-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-111-1-111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111-1-111-1-111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ91111111-1-111-1-1111-1-1-1-1-111-11-1-111-1-111-1-11-1ii−i−i-111111-1-1-1-1iiii−i−i−i−iii−i−ii−iii−i−i11-1-1i−iii−i−i1-1
χ101111111-1-111-1-1111-1-1-1-1-111-11-1-111-1-111-1-11-1ii−i−i-111111-1-1-1-1iiii−i−i−i−i−i−iiii−iii−i−i-1-111−ii−i−iii-11
χ111111111-1-111-1-1111-1-1-1-1-111-11-1-111-1-111-1-11-1−i−iii-111111-1-1-1-1−i−i−i−iiiiiii−i−i−ii−i−iii-1-111i−iii−i−i-11
χ121111111-1-111-1-1111-1-1-1-1-111-11-1-111-1-111-1-11-1−i−iii-111111-1-1-1-1−i−i−i−iiiii−i−iii−ii−i−iii11-1-1−ii−i−iii1-1
χ131111111-1-111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-1-11ii−i−i-1-1-1-1-111111iiii−i−i−i−iii−i−i−ii−i−iii11-1-1i−i−i−iii-11
χ141111111-1-111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-1-11ii−i−i-1-1-1-1-111111iiii−i−i−i−i−i−iii−ii−i−iii-1-111−iiii−i−i1-1
χ151111111-1-111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-1-11−i−iii-1-1-1-1-111111−i−i−i−iiiiiii−i−ii−iii−i−i-1-111i−i−i−iii1-1
χ161111111-1-111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-1-11−i−iii-1-1-1-1-111111−i−i−i−iiiii−i−iiii−iii−i−i11-1-1−iiii−i−i-11
χ17222222222-2-2222222222-200-2-20022-2-2-2-222000000-20000-200000000000022220000000000-2-2000000
χ18222222222-2-2222222222-200-2-20022-2-2-2-222000000-20000-2000000000000-2-2-2-2000000000022000000
χ192222222-2-2-2-2-2-2222-2-2-2-22002-2002222-2-2-2-200000020000-20000000000002i2i−2i−2i0000000000−2i2i000000
χ202222222-2-2-2-2-2-2222-2-2-2-22002-2002222-2-2-2-200000020000-2000000000000−2i−2i2i2i00000000002i−2i000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-22222-11111-11111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-11111-1111111111111000022-1-1-1-1000000000000
χ25222222-1-2-222-2-2-1-1-11111-222-22-2-2-1-111-1-1112-22i2i−2i−2i1-1-1-1-1-11111−i−i−i−iiiii00002i−2i−i−iii000000000000
χ26222222-1-2-222-2-2-1-1-11111-222-22-2-2-1-111-1-1112-2−2i−2i2i2i1-1-1-1-1-11111iiii−i−i−i−i0000−2i2iii−i−i000000000000
χ27222222-1-2-222-2-2-1-1-11111-2-2-2-2222-1-111-1-111-222i2i−2i−2i11111-1-1-1-1-1−i−i−i−iiiii0000−2i2iii−i−i000000000000
χ28222222-1-2-222-2-2-1-1-11111-2-2-2-2222-1-111-1-111-22−2i−2i2i2i11111-1-1-1-1-1iiii−i−i−i−i00002i−2i−i−iii000000000000
χ292222-2-222222-2-22222222-2222-2-2-2-2-22222-2-2-220000-222-2-2-222-2-2000000000000000000000000000000
χ302222-2-222222-2-22222222-2-2-22-222-2-22222-2-22-20000-2-2-222-2-2-222000000000000000000000000000000
χ312222-2-2222-2-2-2-22222222200-2200-2-2-2-2-2-2-2-200000020000200000000000000000000000000002i−2i2i−2i00
χ322222-2-2222-2-2-2-22222222200-2200-2-2-2-2-2-2-2-20000002000020000000000000000000000000000−2i2i−2i2i00
χ332222-2-22-2-22222222-2-2-2-2222-2-222-2-2-2-22222-2-20000222-2-2-2-2-222000000000000000000000000000000
χ342222-2-22-2-22222222-2-2-2-22-2-2-2-2-2-2-2-2-2-222222200002-2-222-222-2-2000000000000000000000000000000
χ352222-2-22-2-2-2-222222-2-2-2-2-2002200-2-222-2-222000000-20000200000000000000000000000000002-2-2200
χ362222-2-22-2-2-2-222222-2-2-2-2-2002200-2-222-2-222000000-2000020000000000000000000000000000-222-200
χ372222-2-2-12222-2-2-1-1-1-1-1-1-1-2222-2-2-211-1-1-1-111-2200001-1-1111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-12222-2-2-1-1-1-1-1-1-1-2222-2-2-211-1-1-1-111-2200001-1-1111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-12222-2-2-1-1-1-1-1-1-1-2-2-22-22211-1-1-1-1112-20000111-1-1111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-12222-2-2-1-1-1-1-1-1-1-2-2-22-22211-1-1-1-1112-20000111-1-1111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-1-2-22222-1-1-11111222-2-2221111-1-1-1-1-2-20000-1-1-111111-1-133−3−3−3−3330000003−3−33000000000000
χ422222-2-2-1-2-22222-1-1-11111222-2-2221111-1-1-1-1-2-20000-1-1-111111-1-1−3−33333−3−3000000−333−3000000000000
χ432222-2-2-1-2-22222-1-1-111112-2-2-2-2-2-21111-1-1-1-1220000-111-1-11-1-11133−3−3−3−333000000−333−3000000000000
χ442222-2-2-1-2-22222-1-1-111112-2-2-2-2-2-21111-1-1-1-1220000-111-1-11-1-111−3−33333−3−30000003−3−33000000000000
χ452-22-22-222i−2i002i−2i2-2-22i2i−2i−2i00000002-200002i−2i001+i−1−i1−i−1+i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000002−2−i2i200000000
χ462-22-22-222i−2i002i−2i2-2-22i2i−2i−2i00000002-200002i−2i001+i−1−i1−i−1+i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−22i2−i200000000
χ472-22-22-222i−2i002i−2i2-2-22i2i−2i−2i00000002-200002i−2i00−1−i1+i−1+i1−i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−22i2−i200000000
χ482-22-22-222i−2i002i−2i2-2-22i2i−2i−2i00000002-200002i−2i00−1−i1+i−1+i1−i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000002−2−i2i200000000
χ492-22-22-22−2i2i00−2i2i2-2-2−2i−2i2i2i00000002-20000−2i2i001−i−1+i1+i−1−i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000002−2i2−i200000000
χ502-22-22-22−2i2i00−2i2i2-2-2−2i−2i2i2i00000002-20000−2i2i001−i−1+i1+i−1−i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−22−i2i200000000
χ512-22-22-22−2i2i00−2i2i2-2-2−2i−2i2i2i00000002-20000−2i2i00−1+i1−i−1−i1+i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−22−i2i200000000
χ522-22-22-22−2i2i00−2i2i2-2-2−2i−2i2i2i00000002-20000−2i2i00−1+i1−i−1−i1+i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000002−2i2−i200000000
χ53444444-244-4-444-2-2-2-2-2-2-2-400-4-400-2-22222-2-20000002000020000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-222224004-400-2-2-2-22222000000-2000020000000000000000000000000000000000
χ554444-4-4-244-4-4-4-4-2-2-2-2-2-2-2400-440022222222000000-20000-20000000000000000000000000000000000
χ564444-4-4-2-4-4-4-444-2-2-22222-400440022-2-222-2-200000020000-20000000000000000000000000000000000
χ574-44-44-4-24i−4i004i−4i-222−2i−2i2i2i0000000-220000−2i2i002+2i−2−2i2−2i−2+2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000
χ584-44-44-4-24i−4i004i−4i-222−2i−2i2i2i0000000-220000−2i2i00−2−2i2+2i−2+2i2−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000
χ594-44-44-4-2−4i4i00−4i4i-2222i2i−2i−2i0000000-2200002i−2i002−2i−2+2i2+2i−2−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000
χ604-44-44-4-2−4i4i00−4i4i-2222i2i−2i−2i0000000-2200002i−2i00−2+2i2−2i−2−2i2+2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000
χ614-44-4-4444i−4i00−4i4i4-4-44i4i−4i−4i0000000-440000−4i4i0000000000000000000000000000000000000000000000
χ624-44-4-444−4i4i004i−4i4-4-4−4i−4i4i4i0000000-4400004i−4i0000000000000000000000000000000000000000000000
χ634-44-4-44-24i−4i00−4i4i-222−2i−2i2i2i00000002-200002i−2i0000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000
χ644-44-4-44-24i−4i00−4i4i-222−2i−2i2i2i00000002-200002i−2i0000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000
χ654-44-4-44-2−4i4i004i−4i-2222i2i−2i−2i00000002-20000−2i2i0000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000
χ664-44-4-44-2−4i4i004i−4i-2222i2i−2i−2i00000002-20000−2i2i0000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000
χ674-4-44004004-400-4-440000000004-400004-400000000000000004-4000000000000000000000000000000
χ684-4-44004004-400-4-44000000000-4400004-40000000000000000-44000000000000000000000000000000
χ694-4-4400400-4400-4-44000004-400000000-440000000004-40000000000000000000000000000000000000
χ704-4-4400400-4400-4-4400000-4400000000-44000000000-440000000000000000000000000000000000000
χ714-4-4400-2004-40022-2−2i32i3−2i32i3000004-400−2i32i3-2200000000000−2i32i3000-22000000000000000000000000000000
χ724-4-4400-2004-40022-2−2i32i3−2i32i300000-4400−2i32i3-22000000000002i3−2i30002-2000000000000000000000000000000
χ734-4-4400-2004-40022-22i3−2i32i3−2i3000004-4002i3−2i3-22000000000002i3−2i3000-22000000000000000000000000000000
χ744-4-4400-2004-40022-22i3−2i32i3−2i300000-44002i3−2i3-2200000000000−2i32i30002-2000000000000000000000000000000
χ754-4-4400-200-440022-2−2i32i3−2i32i304-40000002i3−2i32-2000000000-22000−2i32i300000000000000000000000000000000
χ764-4-4400-200-440022-2−2i32i3−2i32i30-440000002i3−2i32-20000000002-20002i3−2i300000000000000000000000000000000
χ774-4-4400-200-440022-22i3−2i32i3−2i304-4000000−2i32i32-2000000000-220002i3−2i300000000000000000000000000000000
χ784-4-4400-200-440022-22i3−2i32i3−2i30-44000000−2i32i32-20000000002-2000−2i32i300000000000000000000000000000000
χ7988-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000

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