Finite Group Databasebeta

← Group #10691673

Character table — Group #10691673

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order1222223444444666666644488881212121212121212888888121224242424242424242424242424242424888824661212244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ91111111-1-1-1-1-1-11111111-111ii−i−i-1-1-1-1-1-1-1-1ii−i−ii−i11iiii−i−i−i−iiiii−i−i−i−iii−i−i1-111-1-111-1-1i−i11-1-1i−i
χ101111111-1-1-1-1-1-11111111-111ii−i−i-1-1-1-1-1-1-1-1ii−i−ii−i11iiii−i−i−i−iiiii−i−i−i−i−i−iii1-111-1-1-1-111−ii-1-111−ii
χ111111111-1-1-1-1-1-11111111-111ii−i−i-1-1-1-1-1-1-1-1−i−iiii−i11iiii−i−i−i−i−i−i−i−iiiiiii−i−i-11-1-11111-1-1i−i-1-111−ii
χ121111111-1-1-1-1-1-11111111-111ii−i−i-1-1-1-1-1-1-1-1−i−iiii−i11iiii−i−i−i−i−i−i−i−iiiii−i−iii-11-1-111-1-111−ii11-1-1i−i
χ131111111-1-1-1-1-1-11111111-111−i−iii-1-1-1-1-1-1-1-1ii−i−i−ii11−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11-1-111-1-111i−i11-1-1−ii
χ141111111-1-1-1-1-1-11111111-111−i−iii-1-1-1-1-1-1-1-1ii−i−i−ii11−i−i−i−iiiiiiiii−i−i−i−i−i−iii-11-1-11111-1-1−ii-1-111i−i
χ151111111-1-1-1-1-1-11111111-111−i−iii-1-1-1-1-1-1-1-1−i−iii−ii11−i−i−i−iiiii−i−i−i−iiiiiii−i−i1-111-1-1-1-111i−i-1-111i−i
χ161111111-1-1-1-1-1-11111111-111−i−iii-1-1-1-1-1-1-1-1−i−iii−ii11−i−i−i−iiiii−i−i−i−iiiii−i−iii1-111-1-111-1-1−ii11-1-1−ii
χ17222222222-2-2-2-222222222-2-2000022-2-222-2-2000000-2-200000000000000002i2i−2i−2i0000000000−2i2i000000
χ18222222222-2-2-2-222222222-2-2000022-2-222-2-2000000-2-20000000000000000−2i−2i2i2i00000000002i−2i000000
χ192222222-2-222222222222-2-2-20000-2-222-2-222000000-2-2000000000000000022220000000000-2-2000000
χ202222222-2-222222222222-2-2-20000-2-222-2-222000000-2-20000000000000000-2-2-2-2000000000022000000
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
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ25222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2222i2i−2i−2i111111112i2i−2i−2i2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ26222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2222i2i−2i−2i11111111−2i−2i2i2i2i−2i-1-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222−2i−2i2i2i111111112i2i−2i−2i−2i2i-1-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222−2i−2i2i2i11111111−2i−2i2i2i−2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ292222-2-222222-2-2-2-2-2-2222-2-220000-2-22222-2-20000002-2000000000000000000000000002-2-2200000000
χ302222-2-222222-2-2-2-2-2-2222-2-220000-2-22222-2-20000002-200000000000000000000000000-222-200000000
χ312222-2-2222-2-222-2-2-2-2222-22-22222-2-2-2-222220000-2-2-2222-2-222-2-2000000000000000000000000000000
χ322222-2-2222-2-222-2-2-2-2222-22-2-2-2-2-2-2-2-2-22222000022-22-2-222-2-222000000000000000000000000000000
χ332222-2-22-2-222-2-2-2-2-2-222222-22i2i−2i−2i2222-2-2-2-20000−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ342222-2-22-2-222-2-2-2-2-2-222222-2−2i−2i2i2i2222-2-2-2-200002i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ352222-2-22-2-2-2-222-2-2-2-22222-22000022-2-2-2-2220000002-2000000000000000000000000002-22-200000000
χ362222-2-22-2-2-2-222-2-2-2-22222-22000022-2-2-2-2220000002-200000000000000000000000000-22-2200000000
χ372222-2-2-122-2-2221111-1-1-1-22-222221111-1-1-1-10000-2-21-1-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-122-2-2221111-1-1-1-22-222221111-1-1-1-10000-2-21-1-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-122-2-2221111-1-1-1-22-2-2-2-2-21111-1-1-1-10000221-111-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-122-2-2221111-1-1-1-22-2-2-2-2-21111-1-1-1-10000221-111-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-1-2-222-2-21111-1-1-122-22i2i−2i−2i-1-1-1-111110000−2i2i1-1−i−iiiii−i−i33−3−3−3−333000000−i3i3i3−i3000000000000
χ422222-2-2-1-2-222-2-21111-1-1-122-22i2i−2i−2i-1-1-1-111110000−2i2i1-1−i−iiiii−i−i−3−33333−3−3000000i3−i3−i3i3000000000000
χ432222-2-2-1-2-222-2-21111-1-1-122-2−2i−2i2i2i-1-1-1-1111100002i−2i1-1ii−i−i−i−iii33−3−3−3−333000000i3−i3−i3i3000000000000
χ442222-2-2-1-2-222-2-21111-1-1-122-2−2i−2i2i2i-1-1-1-1111100002i−2i1-1ii−i−i−i−iii−3−33333−3−3000000−i3i3i3−i3000000000000
χ4522-2-22-22002i−2i2i−2i22-2-22-2-20000000002i−2i002i−2i1+i−1−i1−i−1+i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002−2−i2i200
χ4622-2-22-22002i−2i2i−2i22-2-22-2-20000000002i−2i002i−2i1+i−1−i1−i−1+i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−22i2−i200
χ4722-2-22-22002i−2i2i−2i22-2-22-2-20000000002i−2i002i−2i−1−i1+i−1+i1−i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−22i2−i200
χ4822-2-22-22002i−2i2i−2i22-2-22-2-20000000002i−2i002i−2i−1−i1+i−1+i1−i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000002−2−i2i200
χ4922-2-22-2200−2i2i−2i2i22-2-22-2-2000000000−2i2i00−2i2i1−i−1+i1+i−1−i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000002−2i2−i200
χ5022-2-22-2200−2i2i−2i2i22-2-22-2-2000000000−2i2i00−2i2i1−i−1+i1+i−1−i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−22−i2i200
χ5122-2-22-2200−2i2i−2i2i22-2-22-2-2000000000−2i2i00−2i2i−1+i1−i−1−i1+i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−22−i2i200
χ5222-2-22-2200−2i2i−2i2i22-2-22-2-2000000000−2i2i00−2i2i−1+i1−i−1−i1+i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002−2i2−i200
χ53444444-244-4-4-4-4-2-2-2-2-2-2-24-4-40000-2-222-2-2220000002200000000000000000000000000000000000000
χ54444444-2-4-44444-2-2-2-2-2-2-2-4-4-4000022-2-222-2-20000002200000000000000000000000000000000000000
χ554444-4-4-24444-4-42222-2-2-2-4-44000022-2-2-2-222000000-2200000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4442222-2-2-24-440000-2-22222-2-2000000-2200000000000000000000000000000000000000
χ5744-4-44-4-2004i−4i4i−4i-2-222-222000000000−2i2i00−2i2i2+2i−2−2i2−2i−2+2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000
χ5844-4-44-4-2004i−4i4i−4i-2-222-222000000000−2i2i00−2i2i−2−2i2+2i−2+2i2−2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000
χ5944-4-44-4-200−4i4i−4i4i-2-222-2220000000002i−2i002i−2i2−2i−2+2i2+2i−2−2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000
χ6044-4-44-4-200−4i4i−4i4i-2-222-2220000000002i−2i002i−2i−2+2i2−2i−2−2i2+2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000
χ6144-4-4-444004i−4i−4i4i-4-4444-4-40000000004i−4i00−4i4i0000000000000000000000000000000000000000000000
χ6244-4-4-44400−4i4i4i−4i-4-4444-4-4000000000−4i4i004i−4i0000000000000000000000000000000000000000000000
χ6344-4-4-44-2004i−4i−4i4i22-2-2-222000000000−2i2i002i−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
χ6444-4-4-44-2004i−4i−4i4i22-2-2-222000000000−2i2i002i−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
χ6544-4-4-44-200−4i4i4i−4i22-2-2-2220000000002i−2i00−2i2i0000000000000000−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
χ6644-4-4-44-200−4i4i4i−4i22-2-2-2220000000002i−2i00−2i2i0000000000000000ζ4+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
χ674-44-40044i−4i00000000-44-40002+2i−2−2i2−2i−2+2i00004i−4i00000000002+2i−2−2i002−2i−2+2i00000000000000000000000000000000
χ684-44-40044i−4i00000000-44-4000−2−2i2+2i−2+2i2−2i00004i−4i0000000000−2−2i2+2i00−2+2i2−2i00000000000000000000000000000000
χ694-44-4004−4i4i00000000-44-40002−2i−2+2i2+2i−2−2i0000−4i4i00000000002−2i−2+2i002+2i−2−2i00000000000000000000000000000000
χ704-44-4004−4i4i00000000-44-4000−2+2i2−2i−2−2i2+2i0000−4i4i0000000000−2+2i2−2i00−2−2i2+2i00000000000000000000000000000000
χ714-44-400-24i−4i0000−2i32i3−2i32i32-220002+2i−2−2i2−2i−2+2i23−2300−2i2i0000000000−1−i1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−1+i1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000000000
χ724-44-400-24i−4i0000−2i32i3−2i32i32-22000−2−2i2+2i−2+2i2−2i23−2300−2i2i00000000001+i−1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ221−i−1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000000000
χ734-44-400-24i−4i00002i3−2i32i3−2i32-220002+2i−2−2i2−2i−2+2i−232300−2i2i0000000000−1−i1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−1+i1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000000000
χ744-44-400-24i−4i00002i3−2i32i3−2i32-22000−2−2i2+2i−2+2i2−2i−232300−2i2i00000000001+i−1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ221−i−1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000000000
χ754-44-400-2−4i4i0000−2i32i3−2i32i32-220002−2i−2+2i2+2i−2−2i−2323002i−2i0000000000−1+i1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−1−i1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000000000
χ764-44-400-2−4i4i0000−2i32i3−2i32i32-22000−2+2i2−2i−2−2i2+2i−2323002i−2i00000000001−i−1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ221+i−1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000000000
χ774-44-400-2−4i4i00002i3−2i32i3−2i32-220002−2i−2+2i2+2i−2−2i23−23002i−2i0000000000−1+i1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−1−i1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000000000
χ784-44-400-2−4i4i00002i3−2i32i3−2i32-22000−2+2i2−2i−2−2i2+2i23−23002i−2i00000000001−i−1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221+i−1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000000000
χ798-8-880080000000000-8-880000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-4000000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-40000004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000

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