Finite Group Databasebeta

← Group #10692764

Character table — Group #10692764

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881212121216161616161624242424242448484848
order122222344446666666444488881212121212121212888888121224242424242424242424242424242424888844121212122444882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91111-1-11-1-1-1-1-1-1111-1-111-11ii−i−i11-1-111-1-1i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1ii−i−ii−iii−i−i11-1-1i−i1-1i−i
χ101111-1-11-1-1-1-1-1-1111-1-111-11ii−i−i11-1-111-1-1i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1−i−iiii−iii−i−i-1-111−ii-11−ii
χ111111-1-11-1-1-1-1-1-1111-1-111-11ii−i−i11-1-111-1-1i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111ii−i−i−ii−i−iii11-1-1i−i-11−ii
χ121111-1-11-1-1-1-1-1-1111-1-111-11ii−i−i11-1-111-1-1i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−iii−ii−i−iii-1-111−ii1-1i−i
χ131111-1-11-1-1-1-1-1-1111-1-111-11−i−iii11-1-111-1-1−ii11-1-11-1−i−i−i−iiiii1111-1-1-1-1ii−i−i−ii−i−iii-1-111i−i-11i−i
χ141111-1-11-1-1-1-1-1-1111-1-111-11−i−iii11-1-111-1-1−ii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−iii−ii−i−iii11-1-1−ii1-1−ii
χ151111-1-11-1-1-1-1-1-1111-1-111-11−i−iii11-1-111-1-1−ii-1-1111-1−i−i−i−iiiii-1-1-1-11111ii−i−ii−iii−i−i-1-111i−i1-1−ii
χ161111-1-11-1-1-1-1-1-1111-1-111-11−i−iii11-1-111-1-1−ii-1-1111-1−i−i−i−iiiii-1-1-1-11111−i−iiii−iii−i−i11-1-1−ii-11i−i
χ17222222222-2-22222222-2-2-220000-2-22222-2-2000000-2-2000000000000000000000000002-2-22000000
χ18222222222-2-22222222-2-2-220000-2-22222-2-2000000-2-200000000000000000000000000-222-2000000
χ192222222-2-22222222222-2-2-2000022-2-2-2-222000000-2-2000000000000000022220000000000-2-20000
χ202222222-2-22222222222-2-2-2000022-2-2-2-222000000-2-20000000000000000-2-2-2-20000000000220000
χ212222222-2-2-2-22222222-222-22i2i−2i−2i-2-2-2-2-2-2-2-2−2i2i0000222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ222222222-2-2-2-22222222-222-2−2i−2i2i2i-2-2-2-2-2-2-2-22i−2i000022−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ23222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
χ24222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-211110000000000
χ25222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-211110000000000
χ26222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-10000000000
χ27222222-1-2-2-2-2-1-1-1-1-1-1-1-222-22i2i−2i−2i11111111−2i2i0000-1-1−i−iii−i−iii33−3−333−3−3000000−i3i3−i3i30000000000
χ28222222-1-2-2-2-2-1-1-1-1-1-1-1-222-22i2i−2i−2i11111111−2i2i0000-1-1−i−iii−i−iii−3−333−3−333000000i3−i3i3−i30000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-1-222-2−2i−2i2i2i111111112i−2i0000-1-1ii−i−iii−i−i33−3−333−3−3000000i3−i3i3−i30000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-1-222-2−2i−2i2i2i111111112i−2i0000-1-1ii−i−iii−i−i−3−333−3−333000000−i3i3−i3i30000000000
χ312222-2-222222-2-2222-2-2-22-2-22222-2-222-2-222-2-200002-222-2-2-2-2220000000000000000000000000000
χ322222-2-222222-2-2222-2-2-22-2-2-2-2-2-2-2-222-2-2222200002-2-2-22222-2-20000000000000000000000000000
χ332222-2-2222-2-2-2-2222-2-22-22-200002222-2-2-2-2000000-2200000000000000002i2i−2i−2i0000000000−2i2i0000
χ342222-2-2222-2-2-2-2222-2-22-22-200002222-2-2-2-2000000-220000000000000000−2i−2i2i2i00000000002i−2i0000
χ352222-2-22-2-222-2-2222-2-2-2-2220000-2-2-2-22222000000-22000000000000000000000000002-22-2000000
χ362222-2-22-2-222-2-2222-2-2-2-2220000-2-2-2-22222000000-2200000000000000000000000000-22-22000000
χ372222-2-2-1222211-1-1-111-22-2-2222211-1-111-1-1-2-20000-11-1-11111-1-133−3−3−3−333000000−333−30000000000
χ382222-2-2-1222211-1-1-111-22-2-2222211-1-111-1-1-2-20000-11-1-11111-1-1−3−33333−3−30000003−3−330000000000
χ392222-2-2-1222211-1-1-111-22-2-2-2-2-2-211-1-111-1-1220000-1111-1-1-1-11133−3−3−3−3330000003−3−330000000000
χ402222-2-2-1222211-1-1-111-22-2-2-2-2-2-211-1-111-1-1220000-1111-1-1-1-111−3−33333−3−3000000−333−30000000000
χ412222-2-2-1-2-2-2-211-1-1-11122-222i2i−2i−2i-1-111-1-1112i−2i22-2-2-11−i−i−i−iiiii-1-1-1-1111100002i−2i−i−iii0000000000
χ422222-2-2-1-2-2-2-211-1-1-11122-222i2i−2i−2i-1-111-1-1112i−2i-2-222-11−i−i−i−iiiii1111-1-1-1-10000−2i2iii−i−i0000000000
χ432222-2-2-1-2-2-2-211-1-1-11122-22−2i−2i2i2i-1-111-1-111−2i2i22-2-2-11iiii−i−i−i−i-1-1-1-111110000−2i2iii−i−i0000000000
χ442222-2-2-1-2-2-2-211-1-1-11122-22−2i−2i2i2i-1-111-1-111−2i2i-2-222-11iiii−i−i−i−i1111-1-1-1-100002i−2i−i−iii0000000000
χ45444444-244-4-4-2-2-2-2-2-2-2-4-4-44000022-2-2-2-22200000022000000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-2-2-2-24-4-4-40000-2-22222-2-200000022000000000000000000000000000000000000
χ474444-4-4-244-4-422-2-2-2224-44-40000-2-2-2-222220000002-2000000000000000000000000000000000000
χ484444-4-4-2-4-44422-2-2-222-4-44400002222-2-2-2-20000002-2000000000000000000000000000000000000
χ4944-4-4004004i−4i004-4-400000000000000004i−4i002-22i−2i00000000002-22-22i−2i2i−2i00000000000000000000
χ5044-4-4004004i−4i004-4-400000000000000004i−4i00-22−2i2i0000000000-22-22−2i2i−2i2i00000000000000000000
χ5144-4-400400−4i4i004-4-40000000000000000−4i4i002-2−2i2i00000000002-22-2−2i2i−2i2i00000000000000000000
χ5244-4-400400−4i4i004-4-40000000000000000−4i4i00-222i−2i0000000000-22-222i−2i2i−2i00000000000000000000
χ5344-4-400-2004i−4i−2i32i3-222−2i32i30000000023−230000−2i2i002-22i−2i0000000000−1+31−3−1−31+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ5444-4-400-2004i−4i−2i32i3-222−2i32i30000000023−230000−2i2i00-22−2i2i00000000001−3−1+31+3−1−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000
χ5544-4-400-2004i−4i2i3−2i3-2222i3−2i300000000−23230000−2i2i002-22i−2i0000000000−1−31+3−1+31−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ5644-4-400-2004i−4i2i3−2i3-2222i3−2i300000000−23230000−2i2i00-22−2i2i00000000001+3−1−31−3−1+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ5744-4-400-200−4i4i−2i32i3-222−2i32i300000000−232300002i−2i002-2−2i2i0000000000−1−31+3−1+31−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ5844-4-400-200−4i4i−2i32i3-222−2i32i300000000−232300002i−2i00-222i−2i00000000001+3−1−31−3−1+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ5944-4-400-200−4i4i2i3−2i3-2222i3−2i30000000023−2300002i−2i002-2−2i2i0000000000−1+31−3−1−31+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000
χ6044-4-400-200−4i4i2i3−2i3-2222i3−2i30000000023−2300002i−2i00-222i−2i00000000001−3−1+31+3−1−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ614-44-40044i−4i0000-44-40000002+2i−2−2i2−2i−2+2i004i−4i0000000000002+2i−2−2i00002−2i−2+2i0000000000000000000000000000
χ624-44-40044i−4i0000-44-4000000−2−2i2+2i−2+2i2−2i004i−4i000000000000−2−2i2+2i0000−2+2i2−2i0000000000000000000000000000
χ634-44-4004−4i4i0000-44-40000002−2i−2+2i2+2i−2−2i00−4i4i0000000000002−2i−2+2i00002+2i−2−2i0000000000000000000000000000
χ644-44-4004−4i4i0000-44-4000000−2+2i2−2i−2−2i2+2i00−4i4i000000000000−2+2i2−2i0000−2−2i2+2i0000000000000000000000000000
χ654-44-400-24i−4i00−2i32i32-222i3−2i300002+2i−2−2i2−2i−2+2i00−2i2i23−230000000000−1−i1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−1+i1−i0000000000000000000000000000
χ664-44-400-24i−4i00−2i32i32-222i3−2i30000−2−2i2+2i−2+2i2−2i00−2i2i23−2300000000001+i−1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ221−i−1+i0000000000000000000000000000
χ674-44-400-24i−4i002i3−2i32-22−2i32i300002+2i−2−2i2−2i−2+2i00−2i2i−23230000000000−1−i1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−1+i1−i0000000000000000000000000000
χ684-44-400-24i−4i002i3−2i32-22−2i32i30000−2−2i2+2i−2+2i2−2i00−2i2i−232300000000001+i−1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ221−i−1+i0000000000000000000000000000
χ694-44-400-2−4i4i00−2i32i32-222i3−2i300002−2i−2+2i2+2i−2−2i002i−2i−23230000000000−1+i1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−1−i1+i0000000000000000000000000000
χ704-44-400-2−4i4i00−2i32i32-222i3−2i30000−2+2i2−2i−2−2i2+2i002i−2i−232300000000001−i−1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ221+i−1−i0000000000000000000000000000
χ714-44-400-2−4i4i002i3−2i32-22−2i32i300002−2i−2+2i2+2i−2−2i002i−2i23−230000000000−1+i1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−1−i1+i0000000000000000000000000000
χ724-44-400-2−4i4i002i3−2i32-22−2i32i30000−2+2i2−2i−2−2i2+2i002i−2i23−2300000000001−i−1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221+i−1−i0000000000000000000000000000
χ734-4-444-44000044-4-44-4-40000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ744-4-444-44000044-4-44-4-400000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ754-4-44-4440000-4-4-4-4444000000000000000000000000000000000000000022−22−22220000000000000000
χ764-4-44-4440000-4-4-4-44440000000000000000000000000000000000000000−222222−220000000000000000
χ778-8-888-8-40000-4-444-444000000000000000000000000000000000000000000000000000000000000
χ788-8-88-88-400004444-4-4-4000000000000000000000000000000000000000000000000000000000000

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