Finite Group Databasebeta

← Group #10694324

Character table — Group #10694324

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222222222344446666666446666121212124444888812121212121212121212242424242424242444444444246612124444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-111-1-1ii−i−iii−i−i1-1
χ1011111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-111-1-1−i−iii−i−iii-11
χ1111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11-1-111ii−i−i−i−iii-11
χ1211111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11-1-111−i−iiiii−i−i1-1
χ1311111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11-1-111−i−iiiii−i−i-11
χ1411111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11-1-111ii−i−i−i−iii1-1
χ1511111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-111-1-1−i−iii−i−iii1-1
χ1611111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-111-1-1ii−i−iii−i−i-11
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2322222222-2-2-2-2222222222222-2-2-2-2-2-2222200000000-2-2000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-2-2-2222222222222-2-2-2-2-2-2222200000000-2-20000000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1110000000000
χ2622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-2211-1-10000000000
χ2722222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i2i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-2211-1-10000000000
χ2822222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1110000000000
χ2922-2-22-2-222-22-2222-2-22-2-2-2-2222-22-2-2222-2-2000000002-20000000000000000000000000000002i−2i2i−2i000000
χ3022-2-22-2-222-22-2222-2-22-2-2-2-2222-22-2-2222-2-2000000002-2000000000000000000000000000000−2i2i−2i2i000000
χ3122-2-22-2-222-22-22-2-2222-2-2-2-222-222-2-22-2-2222-22-20000-2222-2-222-2-200000000000000000000000000000000
χ3222-2-22-2-222-22-22-2-2222-2-2-2-222-222-2-22-2-222-22-220000-22-2-222-2-22200000000000000000000000000000000
χ3322-2-22-2-222-22-2-1-2-222-11111-1-1-22-111-111-1-12-22-200001-1-1-111-1-111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ3422-2-22-2-222-22-2-1-2-222-11111-1-1-22-111-111-1-12-22-200001-1-1-111-1-111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ3522-2-22-2-222-22-2-1-2-222-11111-1-1-22-111-111-1-1-22-2200001-111-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3622-2-22-2-222-22-2-1-2-222-11111-1-1-22-111-111-1-1-22-2200001-111-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ3722-2-22-2-22-22-22222-2-22-2-2-2-222-22-222-222-2-22i−2i−2i2i0000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3822-2-22-2-22-22-22222-2-22-2-2-2-222-22-222-222-2-2−2i2i2i−2i0000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3922-2-22-2-22-22-222-2-2222-2-2-2-2222-2-222-2-2-222000000002-20000000000000000000000000000002-2-22000000
χ4022-2-22-2-22-22-222-2-2222-2-2-2-2222-2-222-2-2-222000000002-2000000000000000000000000000000-222-2000000
χ4122-2-22-2-22-22-22-122-2-2-11111-1-1-221-1-11-1-1112i−2i−2i2i00001-1−i−iiiii−i−i33−3−3−3−3330000000000−i3i3i3−i30000000000
χ4222-2-22-2-22-22-22-122-2-2-11111-1-1-221-1-11-1-1112i−2i−2i2i00001-1−i−iiiii−i−i−3−33333−3−30000000000i3−i3−i3i30000000000
χ4322-2-22-2-22-22-22-122-2-2-11111-1-1-221-1-11-1-111−2i2i2i−2i00001-1ii−i−i−i−iii33−3−3−3−3330000000000i3−i3−i3i30000000000
χ4422-2-22-2-22-22-22-122-2-2-11111-1-1-221-1-11-1-111−2i2i2i−2i00001-1ii−i−i−i−iii−3−33333−3−30000000000−i3i3i3−i30000000000
χ452-22-2-22-2222-2-220000-222-2-22-20022-2-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2002-2002-20000000000−i2i2−i2i200
χ462-22-2-22-2222-2-220000-222-2-22-20022-2-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i200-2200-220000000000i2−i2i2−i200
χ472-22-2-22-2222-2-220000-222-2-22-20022-2-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2002-2002-20000000000i2−i2i2−i200
χ482-22-2-22-2222-2-220000-222-2-22-20022-2-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i200-2200-220000000000−i2i2−i2i200
χ492-22-2-22-22-2-22220000-222-2-22-200-2-222000000002−2−2200000000002−22−2−22−22002-200-2200000000002−2−2200
χ502-22-2-22-22-2-22220000-222-2-22-200-2-222000000002−2−2200000000002−22−2−22−2200-22002-20000000000−222−200
χ512-22-2-22-22-2-22220000-222-2-22-200-2-22200000000−222−20000000000−22−222−22−2002-200-220000000000−222−200
χ522-22-2-22-22-2-22220000-222-2-22-200-2-22200000000−222−20000000000−22−222−22−200-22002-200000000002−2−2200
χ53444444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000220000000000000000000000000000000000000000
χ5444444444-4-4-4-4-24444-2-2-2-2-2-2-2-4-42222-2-2-2-200000000220000000000000000000000000000000000000000
χ55444-4-4-44-4000044i−4i4i−4i44-44-4-4-40000004i−4i4i−4i00000000000000000000000000000000000000000000000000
χ56444-4-4-44-400004−4i4i−4i4i44-44-4-4-4000000−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ57444-4-4-44-40000-24i−4i4i−4i-2-22-2222000000−2i2i−2i2i0000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000000000
χ58444-4-4-44-40000-24i−4i4i−4i-2-22-2222000000−2i2i−2i2i0000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000000000
χ59444-4-4-44-40000-2−4i4i−4i4i-2-22-22220000002i−2i2i−2i0000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000000000
χ60444-4-4-44-40000-2−4i4i−4i4i-2-22-22220000002i−2i2i−2i0000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000000000
χ6144-44-44-4-4000044i−4i−4i4i4-44-44-4-40000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6244-44-44-4-400004−4i4i4i−4i4-44-44-4-4000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6344-44-44-4-40000-24i−4i−4i4i-22-22-222000000−2i2i2i−2i0000000000−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+ζ2200000000000000000000000000000000
χ6444-44-44-4-40000-24i−4i−4i4i-22-22-222000000−2i2i2i−2i0000000000ζ4−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−ζ2200000000000000000000000000000000
χ6544-44-44-4-40000-2−4i4i4i−4i-22-22-2220000002i−2i−2i2i0000000000−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−ζ2200000000000000000000000000000000
χ6644-44-44-4-40000-2−4i4i4i−4i-22-22-2220000002i−2i−2i2i0000000000ζ4+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+ζ2200000000000000000000000000000000
χ6744-4-44-4-444-44-4-244-4-4-22222-2-24-4-222-2-2-22200000000-220000000000000000000000000000000000000000
χ6844-4-44-4-44-44-44-2-4-444-22222-2-24-42-2-2222-2-200000000-220000000000000000000000000000000000000000
χ694-4444-4-4-4000040000-44-4-44-4400000000000000000000000000000000000000004i−4i000000000000000000
χ704-4444-4-4-4000040000-44-4-44-440000000000000000000000000000000000000000−4i4i000000000000000000
χ714-44-4-44-4444-4-4-200002-2-222-2200-2-22200000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ724-44-4-44-4444-4-4-200002-2-222-2200-2-222000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ734-44-4-44-44-4-444-200002-2-222-220022-2-20000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ744-44-4-44-44-4-444-200002-2-222-220022-2-200000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ754-4-44-4-4444-4-4440000-4-4-4444-4004-44-4000000000000000000000000000000000000000000000000000000
χ764-4-44-4-4444-4-44-20000222-2-2-2200-22-2200000000000000000000006−6−666−6−66000000000000000000000000
χ774-4-44-4-4444-4-44-20000222-2-2-2200-22-220000000000000000000000−666−6−666−6000000000000000000000000
χ784-4-44-4-444-444-440000-4-4-4444-400-44-44000000000000000000000000000000000000000000000000000000
χ794-4-44-4-444-444-4-20000222-2-2-22002-22-20000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ804-4-44-4-444-444-4-20000222-2-2-22002-22-20000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ814-4-4-4444-4000040000-4-444-4-440000000000000000000000000000000000004-40000000000000000000000
χ824-4-4-4444-4000040000-4-444-4-44000000000000000000000000000000000000-440000000000000000000000
χ838-8888-8-8-80000-400004-444-44-4000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-80000-4000044-4-444-4000000000000000000000000000000000000000000000000000000000000

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