Finite Group Databasebeta

← Group #10691463

Character table — Group #10691463

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12224444223444444666121212124466121212121212444488881212121212121212121224242424242424244444444444121212122244888888
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
χ91111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-11111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-111-1-11-11-111-1-1i−i
χ101111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-11111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii1-111-1-1-11-11-1-111−ii
χ111111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-11111-1-1ii−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−iii−i−i-11-1-1111-11-1-1-111−ii
χ121111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-11111-1-1ii−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii−i−iii-11-1-111-11-1111-1-1i−i
χ131111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-11111-1-1−i−iiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−iii−i−i-11-1-111-11-1111-1-1−ii
χ141111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-11111-1-1−i−iiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−iii-11-1-1111-11-1-1-111i−i
χ151111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-11111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i1-111-1-1-11-11-1-111i−i
χ161111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-11111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-111-1-11-11-111-1-1−ii
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-200000000-2-200000000000000002222-2-2-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-200000000-2-20000000000000000-2-2-2-222220000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2322222222-2-22-2-222222222222-2-2-2-2-2-2222200000000-2-20000000000000000000000000000002-2-22000000
χ2422222222-2-22-2-222222222222-2-2-2-2-2-2222200000000-2-2000000000000000000000000000000-222-2000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22i−2i2i−2i0000222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2−2i2i−2i2i000022−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2722222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i−2i2i−2i0000-1-1−i−iii−i−iii33−3−333−3−30000000000−i3i3−i3i30000000000
χ2822222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i−2i2i−2i0000-1-1−i−iii−i−iii−3−333−3−3330000000000i3−i3i3−i30000000000
χ2922222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i2i−2i2i0000-1-1ii−i−iii−i−i33−3−333−3−30000000000i3−i3i3−i30000000000
χ3022222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i2i−2i2i0000-1-1ii−i−iii−i−i−3−333−3−3330000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-22-222-2-2-2-2222-2-2200002-222-2-2-2-22200000000000000000000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-22-222-2-2-2-222-222-200002-2-2-22222-2-200000000000000000000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-2-2222-2-222-2-200000000-2200000000000000000000000000000022-2-2000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-2222-2-222-2-200000000-22000000000000000000000000000000-2-222000000
χ352222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-11111-1-12-2-220000-11-1-11111-1-1−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i30000000000
χ362222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-11111-1-12-2-220000-11-1-11111-1-1i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i30000000000
χ372222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-11111-1-1-222-20000-1111-1-1-1-111−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i30000000000
χ382222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-11111-1-1-222-20000-1111-1-1-1-111i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i30000000000
χ392222-2-2-2-2-2-222222-2-2222-2-2-2-2-22-2-222-2-22200000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2-2-222222-2-2222-2-2-2-2-22-2-222-2-22200000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2-2-2-122-2-222-1-1-111112-211-1-1-1-1112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1110000000000
χ422222-2-2-2-2-2-2-122-2-222-1-1-111112-211-1-1-1-1112i2i−2i−2i−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i00000000-2211-1-10000000000
χ432222-2-2-2-2-2-2-122-2-222-1-1-111112-211-1-1-1-111−2i−2i2i2i2i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii00000000-2211-1-10000000000
χ442222-2-2-2-2-2-2-122-2-222-1-1-111112-211-1-1-1-111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1110000000000
χ452-2-2222-2-2-2222-200002-2-222-2-200-222-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i200002-22-20000000000−i2i2−i2i200
χ462-2-2222-2-2-2222-200002-2-222-2-200-222-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000-22-220000000000i2−i2i2−i200
χ472-2-2222-2-2-2222-200002-2-222-2-200-222-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i200002-22-20000000000i2−i2i2−i200
χ482-2-2222-2-2-2222-200002-2-222-2-200-222-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000-22-220000000000−i2i2−i2i200
χ492-2-22-2-2222-222-200002-2-2-2-222002-22-2000000002−2−2200000000002−22−2−22−2200002i−2i−2i2i0000000000−i2i2i2−i200
χ502-2-22-2-2222-222-200002-2-2-2-222002-22-2000000002−2−2200000000002−22−2−22−220000−2i2i2i−2i0000000000i2−i2−i2i200
χ512-2-22-2-2222-222-200002-2-2-2-222002-22-200000000−222−20000000000−22−222−22−200002i−2i−2i2i0000000000i2−i2−i2i200
χ522-2-22-2-2222-222-200002-2-2-2-222002-22-200000000−222−20000000000−22−222−22−20000−2i2i2i−2i0000000000−i2i2i2−i200
χ534444444444-244-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000220000000000000000000000000000000000000000
χ5444444444-4-4-2-4-44444-2-2-2-2-2-2-2-4-42222-2-2-2-200000000220000000000000000000000000000000000000000
χ554444-4-4-4-444-2-4-4-4-444-2-2-22222-44-2-222-2-222000000002-20000000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-24444-4-4-2-2-22222-4422-2-222-2-2000000002-20000000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i004000000-44-44i−4i4i−4i0000000000000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ5844-4-44i−4i4i−4i004000000-44-44i−4i4i−4i000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ5944-4-4−4i4i−4i4i004000000-44-4−4i4i−4i4i0000000000000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ6044-4-4−4i4i−4i4i004000000-44-4−4i4i−4i4i000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ614-44-44i−4i−4i4i004004i−4i4-4-4-444i−4i−4i4i0000004-44i−4i00000000000000000000000000000000000000000000000000
χ624-44-44i−4i−4i4i00400−4i4i-44-4-444i−4i−4i4i000000-44−4i4i00000000000000000000000000000000000000000000000000
χ634-44-44i−4i−4i4i00-2004i−4i4-422-2−2i2i2i−2i000000-22−2i2i0000000000−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
χ644-44-44i−4i−4i4i00-2004i−4i4-422-2−2i2i2i−2i000000-22−2i2i0000000000ζ4−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
χ654-44-44i−4i−4i4i00-200−4i4i-4422-2−2i2i2i−2i0000002-22i−2i0000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000000000
χ664-44-44i−4i−4i4i00-200−4i4i-4422-2−2i2i2i−2i0000002-22i−2i0000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000000000
χ674-44-4−4i4i4i−4i004004i−4i-44-4-44−4i4i4i−4i000000-444i−4i00000000000000000000000000000000000000000000000000
χ684-44-4−4i4i4i−4i00400−4i4i4-4-4-44−4i4i4i−4i0000004-4−4i4i00000000000000000000000000000000000000000000000000
χ694-44-4−4i4i4i−4i00-2004i−4i-4422-22i−2i−2i2i0000002-2−2i2i0000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000000000
χ704-44-4−4i4i4i−4i00-2004i−4i-4422-22i−2i−2i2i0000002-2−2i2i0000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000000000
χ714-44-4−4i4i4i−4i00-200−4i4i4-422-22i−2i−2i2i000000-222i−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
χ724-44-4−4i4i4i−4i00-200−4i4i4-422-22i−2i−2i2i000000-222i−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
χ734-4-4444-4-44-44-4400004-4-444-4-4004-4-44000000000000000000000000000000000000000000000000000000
χ744-4-4444-4-44-4-2-440000-222-2-22200-222-20000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ754-4-4444-4-44-4-2-440000-222-2-22200-222-20000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ764-4-4444-4-4-44-24-40000-222-2-222002-2-2200000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ774-4-4444-4-4-44-24-40000-222-2-222002-2-22000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ784-4-44-4-4444-4-24-40000-22222-2-200-22-220000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ794-4-44-4-4444-4-24-40000-22222-2-200-22-2200000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ804-4-44-4-444-444-4400004-4-4-4-44400-44-44000000000000000000000000000000000000000000000000000000
χ814-4-44-4-444-44-2-440000-22222-2-2002-22-200000000000000000000006−6−66−666−6000000000000000000000000
χ824-4-44-4-444-44-2-440000-22222-2-2002-22-20000000000000000000000−666−66−6−66000000000000000000000000
χ8388-8-88i−8i8i−8i00-40000004-44−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ8488-8-8−8i8i−8i8i00-40000004-444i−4i4i−4i000000000000000000000000000000000000000000000000000000000000

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