Finite Group Databasebeta

← Group #10691000

Character table — Group #10691000

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order122234444444466624466121212121212121244448888121212121212121212124444888824661212242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ611111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1
χ911111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−i11-1-1ii−i−i1-111-1-1ii−i−i-11ii−i−ii−i1-1
χ1011111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−i-1-111−i−iii1-111-1-1ii−i−i1-1−i−iii−ii-11
χ1111111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i11-1-1−i−iii-11-1-111−i−iii-11ii−i−i−ii-11
χ1211111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i-1-111ii−i−i-11-1-111−i−iii1-1−i−iiii−i1-1
χ1311111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiii11-1-1ii−i−i-11-1-111ii−i−i-11−i−iiii−i-11
χ1411111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiii-1-111−i−iii-11-1-111ii−i−i1-1ii−i−i−ii1-1
χ1511111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−iii-11−i−iii−ii1-1
χ1611111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii-1-111ii−i−i1-111-1-1−i−iii1-1ii−i−ii−i-11
χ17222222222-2-222222-2-2-2-2-222-2-2222200000000-2-200000000222200000000000000-2-200000000
χ18222222222-2-222222-2-2-2-2-222-2-2222200000000-2-200000000-2-2-2-2000000000000002200000000
χ192222222-2-222-2-2222-22-2-2-2-2-22222-2-200002i−2i2i−2i2-200000000000000000000002i−2i2i−2i0000000000
χ202222222-2-222-2-2222-22-2-2-2-2-22222-2-20000−2i2i−2i2i2-20000000000000000000000−2i2i−2i2i0000000000
χ212222222-2-2-2-2-2-22222-2222-2-2-2-222-2-200000000-220000000000002i2i−2i−2i0000000000000000−2i2i00
χ222222222-2-2-2-2-2-22222-2222-2-2-2-222-2-200000000-22000000000000−2i−2i2i2i00000000000000002i−2i00
χ2322222-2-22222-2-22222-2-2222222-2-2-2-200000000-2-20000000022-2-2000000000000002-200000000
χ2422222-2-22222-2-22222-2-2222222-2-2-2-200000000-2-200000000-2-22200000000000000-2200000000
χ2522222-2-2-2-22222222-2-22-2-2-2-222-2-22200000000-2200000000000022220000000000000000-2-200
χ2622222-2-2-2-22222222-2-22-2-2-2-222-2-22200000000-22000000000000-2-2-2-200000000000000002200
χ2722222-2-2-2-2-2-22222222-222-2-2-2-2-2-22200002-2-222-200000000000000000000002-2-220000000000
χ2822222-2-2-2-2-2-22222222-222-2-2-2-2-2-2220000-222-22-20000000000000000000000-222-20000000000
χ292222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ302222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ312222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-11111111100000000-2-21111-1-1-1-10000000000
χ322222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000022-1-1-1-111110000000000
χ332222-122-2-222-2-2-1-1-1-22-21111-1-1-1-11100002i−2i2i−2i-1133−3−333−3−30000000000−i3i3−i3i3−ii−ii0000000000
χ342222-122-2-222-2-2-1-1-1-22-21111-1-1-1-11100002i−2i2i−2i-11−3−333−3−3330000000000i3−i3i3−i3−ii−ii0000000000
χ352222-122-2-222-2-2-1-1-1-22-21111-1-1-1-1110000−2i2i−2i2i-1133−3−333−3−30000000000i3−i3i3−i3i−ii−i0000000000
χ362222-122-2-222-2-2-1-1-1-22-21111-1-1-1-1110000−2i2i−2i2i-11−3−333−3−3330000000000−i3i3−i3i3i−ii−i0000000000
χ372222-1-2-222-2-2-2-2-1-1-1-22211-1-11111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii000000002-2-1-111−i−iii0000000000
χ382222-1-2-222-2-2-2-2-1-1-1-22211-1-11111112i2i−2i−2i−2i−2i2i2i-1-1−i−i−i−iiiii00000000-2211-1-1ii−i−i0000000000
χ392222-1-2-222-2-2-2-2-1-1-1-22211-1-1111111−2i−2i2i2i2i2i−2i−2i-1-1iiii−i−i−i−i00000000-2211-1-1−i−iii0000000000
χ402222-1-2-222-2-2-2-2-1-1-1-22211-1-1111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−i000000002-2-1-111ii−i−i0000000000
χ412222-1-2-2-2-2-2-222-1-1-122-2-1-1111111-1-100002-2-22-11−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i3-111-10000000000
χ422222-1-2-2-2-2-2-222-1-1-122-2-1-1111111-1-100002-2-22-11i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i3-111-10000000000
χ432222-1-2-2-2-2-2-222-1-1-122-2-1-1111111-1-10000-222-2-11−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i31-1-110000000000
χ442222-1-2-2-2-2-2-222-1-1-122-2-1-1111111-1-10000-222-2-11i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i31-1-110000000000
χ4522-2-222i−2i2-2002i−2i2-2-2000002-2002i−2i2i−2i1+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i00000000000000001+i−1−i1−i−1+i0000
χ4622-2-222i−2i2-2002i−2i2-2-2000002-2002i−2i2i−2i1+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i0000000000000000−1−i1+i−1+i1−i0000
χ4722-2-222i−2i2-2002i−2i2-2-2000002-2002i−2i2i−2i−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i0000000000000000−1−i1+i−1+i1−i0000
χ4822-2-222i−2i2-2002i−2i2-2-2000002-2002i−2i2i−2i−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i00000000000000001+i−1−i1−i−1+i0000
χ4922-2-22−2i2i2-200−2i2i2-2-2000002-200−2i2i−2i2i1−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i00000000000000001−i−1+i1+i−1−i0000
χ5022-2-22−2i2i2-200−2i2i2-2-2000002-200−2i2i−2i2i1−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i0000000000000000−1+i1−i−1−i1+i0000
χ5122-2-22−2i2i2-200−2i2i2-2-2000002-200−2i2i−2i2i−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i0000000000000000−1+i1−i−1−i1+i0000
χ5222-2-22−2i2i2-200−2i2i2-2-2000002-200−2i2i−2i2i−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i00000000000000001−i−1+i1+i−1−i0000
χ534444-24444-4-444-2-2-2-4-4-422-2-222-2-2-2-20000000022000000000000000000000000000000000000
χ544444-244-4-4-4-4-4-4-2-2-24-44-2-22222-2-222000000002-2000000000000000000000000000000000000
χ554444-2-4-44444-4-4-2-2-24-4-4-2-2-2-2-2-222220000000022000000000000000000000000000000000000
χ564444-2-4-4-4-44444-2-2-2-4-442222-2-222-2-2000000002-2000000000000000000000000000000000000
χ5744-4-444i−4i-4400−4i4i4-4-400000-44004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5844-4-44−4i4i-44004i−4i4-4-400000-4400−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5944-4-4-24i−4i4-4004i−4i-22200000-2200−2i2i−2i2i2+2i−2−2i2−2i−2+2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000
χ6044-4-4-24i−4i4-4004i−4i-22200000-2200−2i2i−2i2i−2−2i2+2i−2+2i2−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000
χ6144-4-4-24i−4i-4400−4i4i-222000002-200−2i2i2i−2i0000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000000000
χ6244-4-4-24i−4i-4400−4i4i-222000002-200−2i2i2i−2i0000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000000000
χ6344-4-4-2−4i4i4-400−4i4i-22200000-22002i−2i2i−2i2−2i−2+2i2+2i−2−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000
χ6444-4-4-2−4i4i4-400−4i4i-22200000-22002i−2i2i−2i−2+2i2−2i−2−2i2+2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000
χ6544-4-4-2−4i4i-44004i−4i-222000002-2002i−2i−2i2i0000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000000000
χ6644-4-4-2−4i4i-44004i−4i-222000002-2002i−2i−2i2i0000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000000000
χ674-44-4400004i−4i00-44-400000004i−4i000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ684-44-4400004i−4i00-44-400000004i−4i00000000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ694-44-440000−4i4i00-44-40000000−4i4i000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ704-44-440000−4i4i00-44-40000000−4i4i00000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ718-88-8-400008i−8i004-440000000−4i4i00000000000000000000000000000000000000000000000000
χ728-88-8-40000−8i8i004-4400000004i−4i00000000000000000000000000000000000000000000000000
χ738-8-88800000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-88-40000000044-4000−4i34i3000000000000000000000000000000000000000000000000000000
χ758-8-88-40000000044-40004i3−4i3000000000000000000000000000000000000000000000000000000

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