Finite Group Databasebeta

← Group #10691320

Character table — Group #10691320

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122244443444444446661212121224121212121212121268888888812242424242424242424242424242424248888888888242424242444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-1-111-1-1ii−i−i11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−iii−i−i1-11-1ii−i−i1-1
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-1-111-1-1ii−i−i11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−iii−i−i-11-11−i−iii-11
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-1-111-1-1−i−iii11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−ii−i−iii-11-11ii−i−i-11
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-1-111-1-1−i−iii11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−i−iii1-11-1−i−iii1-1
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-111ii−i−i1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−i−iii1-11-1−i−iii-11
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-111ii−i−i1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−ii−i−iii-11-11ii−i−i1-1
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-111−i−iii1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−iii−i−i-11-11−i−iii1-1
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-111−i−iii1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−iii−i−i1-11-1ii−i−i-11
χ1722222222222-2-2-2-2222222222-2-222-2-2-2-222-200000000-2000000000000000022-2-222-2-20000000000000000
χ1822222222222-2-2-2-2222222222-2-222-2-2-2-222-200000000-20000000000000000-2-222-2-2220000000000000000
χ19222222222-2-22222-2-22222222-2-2-2-22222-2-2-200000000-200000000000000000000000000000022-2-2000000
χ20222222222-2-22222-2-22222222-2-2-2-22222-2-2-200000000-2000000000000000000000000000000-2-222000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2200002i−2i2i−2i2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-220000−2i2i−2i2i200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-22222-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-111111111111111110000000022-1-1-1-10000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-100002i−2i2i−2i-133−3−333−3−3−i−iii−i−iii0000000000−i3i3−i3i30000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-100002i−2i2i−2i-1−3−333−3−333−i−iii−i−iii0000000000i3−i3i3−i30000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-10000−2i2i−2i2i-133−3−333−3−3ii−i−iii−i−i0000000000i3−i3i3−i30000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-10000−2i2i−2i2i-1−3−333−3−333ii−i−iii−i−i0000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-22-22222-2-2-2-2200000000-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-22-22222-2-2-2-2200000000-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-22-2-222-2-222222-2-2-2-22-2-2-2-2-22222200000000-20000000000000000000000000000002-2-22000000
χ342222-2-2-2-22-2-222-2-222222-2-2-2-22-2-2-2-2-22222200000000-2000000000000000000000000000000-222-2000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-222-2-222-200002-2-2220000000022-2-2-2-222000000000000000000000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-222-2-222-20000-222-2200000000-2-22222-2-2000000000000000000000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-111-1-111122-2-22i2i−2i−2i-1-1-1-1-11111−i−i−i−iiiii000000002i−2i−i−iii0000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-111-1-111122-2-2−2i−2i2i2i-1-1-1-1-11111iiii−i−i−i−i00000000−2i2iii−i−i0000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-111-1-1111-2-2222i2i−2i−2i-11111-1-1-1-1−i−i−i−iiiii00000000−2i2iii−i−i0000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-111-1-1111-2-222−2i−2i2i2i-11111-1-1-1-1iiii−i−i−i−i000000002i−2i−i−iii0000000000
χ412222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211-1-111-1-1100002-2-22-133−3−3−3−333-1-11111-1-10000000000−333−30000000000
χ422222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211-1-111-1-1100002-2-22-1−3−33333−3−3-1-11111-1-100000000003−3−330000000000
χ432222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211-1-111-1-110000-222-2-133−3−3−3−33311-1-1-1-11100000000003−3−330000000000
χ442222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211-1-111-1-110000-222-2-1−3−33333−3−311-1-1-1-1110000000000−333−30000000000
χ452-22-22i−2i2i−2i22-200002i−2i2-2-22i−2i2i−2i002-200002i−2i02−2−i2i2000002−22−2−i2i2−i2i200000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000001+i−1−i1−i−1+i00
χ462-22-22i−2i2i−2i22-200002i−2i2-2-22i−2i2i−2i002-200002i−2i02−2−i2i2000002−22−2−i2i2−i2i20000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−1−i1+i−1+i1−i00
χ472-22-22i−2i2i−2i22-200002i−2i2-2-22i−2i2i−2i002-200002i−2i0−22i2−i200000−22−22i2−i2i2−i200000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000−1−i1+i−1+i1−i00
χ482-22-22i−2i2i−2i22-200002i−2i2-2-22i−2i2i−2i002-200002i−2i0−22i2−i200000−22−22i2−i2i2−i20000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000001+i−1−i1−i−1+i00
χ492-22-2−2i2i−2i2i22-20000−2i2i2-2-2−2i2i−2i2i002-20000−2i2i02−2i2−i2000002−22−2i2−i2i2−i20000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000001−i−1+i1+i−1−i00
χ502-22-2−2i2i−2i2i22-20000−2i2i2-2-2−2i2i−2i2i002-20000−2i2i02−2i2−i2000002−22−2i2−i2i2−i200000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000−1+i1−i−1−i1+i00
χ512-22-2−2i2i−2i2i22-20000−2i2i2-2-2−2i2i−2i2i002-20000−2i2i0−22−i2i200000−22−22−i2i2−i2i20000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−1+i1−i−1−i1+i00
χ522-22-2−2i2i−2i2i22-20000−2i2i2-2-2−2i2i−2i2i002-20000−2i2i0−22−i2i200000−22−22−i2i2−i2i200000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000001−i−1+i1+i−1−i00
χ5344444444-244-4-4-4-444-2-2-2-2-2-2-2-4-4-2-22222-2-220000000020000000000000000000000000000000000000000
χ5444444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22220000000020000000000000000000000000000000000000000
χ554444-4-4-4-4-244-4-444-4-4-2-2-222224-4-2-2-2-22222-20000000020000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-444-4-444-2-2-222224-42222-2-2-2-2-20000000020000000000000000000000000000000000000000
χ5744-4-444-4-4400000000-44-444-4-400000000000000000000000000000000000022−220022−22000000000000000000
χ5844-4-444-4-4400000000-44-444-4-4000000000000000000000000000000000000−222200−2222000000000000000000
χ5944-4-4-4-444400000000-44-4-4-444000000000000000000000000000000000000−2i22i2002i2−2i2000000000000000000
χ6044-4-4-4-444400000000-44-4-4-4440000000000000000000000000000000000002i2−2i200−2i22i2000000000000000000
χ614-44-44i−4i4i−4i4-440000−4i4i4-4-44i−4i4i−4i00-440000−4i4i00000000000000000000000000000000000000000000000000
χ624-44-44i−4i4i−4i-24-400004i−4i-222−2i2i−2i2i00-220000−2i2i022−22−2i22i200000−22−22i2−i2i2−i200000000000000000000000000000000
χ634-44-44i−4i4i−4i-24-400004i−4i-222−2i2i−2i2i00-220000−2i2i0−22222i2−2i2000002−22−2−i2i2−i2i200000000000000000000000000000000
χ644-44-44i−4i4i−4i-2-440000−4i4i-222−2i2i−2i2i002-200002i−2i00000000006−6−66−i6i6i6−i600000000000000000000000000000000
χ654-44-44i−4i4i−4i-2-440000−4i4i-222−2i2i−2i2i002-200002i−2i0000000000−666−6i6−i6−i6i600000000000000000000000000000000
χ664-44-4−4i4i−4i4i4-4400004i−4i4-4-4−4i4i−4i4i00-4400004i−4i00000000000000000000000000000000000000000000000000
χ674-44-4−4i4i−4i4i-24-40000−4i4i-2222i−2i2i−2i00-2200002i−2i022−222i2−2i200000−22−22−i2i2−i2i200000000000000000000000000000000
χ684-44-4−4i4i−4i4i-24-40000−4i4i-2222i−2i2i−2i00-2200002i−2i0−2222−2i22i2000002−22−2i2−i2i2−i200000000000000000000000000000000
χ694-44-4−4i4i−4i4i-2-4400004i−4i-2222i−2i2i−2i002-20000−2i2i00000000006−6−66i6−i6−i6i600000000000000000000000000000000
χ704-44-4−4i4i−4i4i-2-4400004i−4i-2222i−2i2i−2i002-20000−2i2i0000000000−666−6−i6i6i6−i600000000000000000000000000000000
χ714-4-444i−4i−4i4i4004-44i−4i00-4-444i−4i−4i4i00004i−4i4-40000000000000000000000000000000000000000000000000000
χ724-4-444i−4i−4i4i400-44−4i4i00-4-444i−4i−4i4i0000−4i4i-440000000000000000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i-2004-44i−4i0022-2−2i2i2i−2i0000−2i2i-2200000000000000000000−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−ζ22000000000000000000000000
χ744-4-444i−4i−4i4i-2004-44i−4i0022-2−2i2i2i−2i0000−2i2i-2200000000000000000000ζ4−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+ζ22000000000000000000000000
χ754-4-444i−4i−4i4i-200-44−4i4i0022-2−2i2i2i−2i00002i−2i2-200000000000000000000−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+ζ22000000000000000000000000
χ764-4-444i−4i−4i4i-200-44−4i4i0022-2−2i2i2i−2i00002i−2i2-200000000000000000000ζ4+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−ζ22000000000000000000000000
χ774-4-44−4i4i4i−4i4004-4−4i4i00-4-44−4i4i4i−4i0000−4i4i4-40000000000000000000000000000000000000000000000000000
χ784-4-44−4i4i4i−4i400-444i−4i00-4-44−4i4i4i−4i00004i−4i-440000000000000000000000000000000000000000000000000000
χ794-4-44−4i4i4i−4i-2004-4−4i4i0022-22i−2i−2i2i00002i−2i-2200000000000000000000−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+ζ22000000000000000000000000
χ804-4-44−4i4i4i−4i-2004-4−4i4i0022-22i−2i−2i2i00002i−2i-2200000000000000000000ζ4+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−ζ22000000000000000000000000
χ814-4-44−4i4i4i−4i-200-444i−4i0022-22i−2i−2i2i0000−2i2i2-200000000000000000000−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−ζ22000000000000000000000000
χ824-4-44−4i4i4i−4i-200-444i−4i0022-22i−2i−2i2i0000−2i2i2-200000000000000000000ζ4−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+ζ22000000000000000000000000
χ8388-8-888-8-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8-888-4000000004-4444-4-4000000000000000000000000000000000000000000000000000000000000

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