Finite Group Databasebeta

← Group #10692279

Character table — Group #10692279

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881212121216161616161624242424242448484848
order122234444446661212121224448888121212121212121268888881224242424242424242424242424242424224488242424244488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ91111111-1-1-1-1111111111-1-1ii−i−i-1-1-1-1-1-1-1-11i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-11-1ii−i−i1-1i−i
χ101111111-1-1-1-1111111111-1-1ii−i−i-1-1-1-1-1-1-1-11i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-1-11−i−iii-11−ii
χ111111111-1-1-1-1111111111-1-1ii−i−i-1-1-1-1-1-1-1-11i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-1111-1ii−i−i-11−ii
χ121111111-1-1-1-1111111111-1-1ii−i−i-1-1-1-1-1-1-1-11i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-111-11−i−iii1-1i−i
χ131111111-1-1-1-1111111111-1-1−i−iii-1-1-1-1-1-1-1-11−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-1111-1−i−iii-11i−i
χ141111111-1-1-1-1111111111-1-1−i−iii-1-1-1-1-1-1-1-11−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-111-11ii−i−i1-1−ii
χ151111111-1-1-1-1111111111-1-1−i−iii-1-1-1-1-1-1-1-11−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-11-1−i−iii1-1−ii
χ161111111-1-1-1-1111111111-1-1−i−iii-1-1-1-1-1-1-1-11−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-1-11ii−i−i-11i−i
χ17222222222-2-22222222-2-2-22000022-2-222-2-2-2000000-2000000000000000022-2-2000000-2200000000
χ18222222222-2-22222222-2-2-22000022-2-222-2-2-2000000-20000000000000000-2-2220000002-200000000
χ192222222-2-2222222222-2-22-20000-2-222-2-222-2000000-200000000000000002222000000-2-200000000
χ202222222-2-2222222222-2-22-20000-2-222-2-222-2000000-20000000000000000-2-2-2-20000002200000000
χ2122222-2-22222222-2-2-2-2-22-2-2222222-2-2-2-222-2-2-20000222-2-222-2-20000000000000000000000000000
χ2222222-2-22222222-2-2-2-2-22-2-2-2-2-2-222-2-2-2-222-22200002-2-222-2-2220000000000000000000000000000
χ2322222-2-222-2-2222-2-2-2-22-22-200002222-2-2-2-22000000-200000000000000000000000000002i−2i2i−2i0000
χ2422222-2-222-2-2222-2-2-2-22-22-200002222-2-2-2-22000000-20000000000000000000000000000−2i2i−2i2i0000
χ2522222-2-2-2-222222-2-2-2-22-2-220000-2-2-2-222222000000-200000000000000000000000000002-2-220000
χ2622222-2-2-2-222222-2-2-2-22-2-220000-2-2-2-222222000000-20000000000000000000000000000-222-20000
χ2722222-2-2-2-2-2-2222-2-2-2-2-22222i2i−2i−2i-2-22222-2-2-2−2i2i000022i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ2822222-2-2-2-2-2-2222-2-2-2-2-2222−2i−2i2i2i-2-22222-2-2-22i−2i00002−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1111111110000-2-211110000000000
χ312222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-22222-111111111-1-1-1-1-1-1-1-10000-2-211110000000000
χ322222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-11111111111111111000022-1-1-1-10000000000
χ332222-122-2-2-2-2-1-1-1-1-1-1-122-2-22i2i−2i−2i11111111-12i−2i2i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-1110000000000
χ342222-122-2-2-2-2-1-1-1-1-1-1-122-2-22i2i−2i−2i11111111-12i−2i−2i−2i2i2i-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-10000000000
χ352222-122-2-2-2-2-1-1-1-1-1-1-122-2-2−2i−2i2i2i11111111-1−2i2i2i2i−2i−2i-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-10000000000
χ362222-122-2-2-2-2-1-1-1-1-1-1-122-2-2−2i−2i2i2i11111111-1−2i2i−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-1110000000000
χ372222-1-2-22222-1-1-11111-22-2-22222-1-11111-1-11-2-20000-1-1-111-1-11133−3−333−3−30000003−33−30000000000
χ382222-1-2-22222-1-1-11111-22-2-22222-1-11111-1-11-2-20000-1-1-111-1-111−3−333−3−333000000−33−330000000000
χ392222-1-2-22222-1-1-11111-22-2-2-2-2-2-2-1-11111-1-11220000-111-1-111-1-133−3−333−3−3000000−33−330000000000
χ402222-1-2-22222-1-1-11111-22-2-2-2-2-2-2-1-11111-1-11220000-111-1-111-1-1−3−333−3−3330000003−33−30000000000
χ412222-1-2-2-2-2-2-2-1-1-11111-22222i2i−2i−2i11-1-1-1-1111−2i2i0000-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000−333−30000000000
χ422222-1-2-2-2-2-2-2-1-1-11111-22222i2i−2i−2i11-1-1-1-1111−2i2i0000-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000003−3−330000000000
χ432222-1-2-2-2-2-2-2-1-1-11111-2222−2i−2i2i2i11-1-1-1-11112i−2i0000-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000003−3−330000000000
χ442222-1-2-2-2-2-2-2-1-1-11111-2222−2i−2i2i2i11-1-1-1-11112i−2i0000-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000−333−30000000000
χ454444-24444-4-4-2-2-2-2-2-2-2-4-4-440000-2-222-2-22220000002000000000000000000000000000000000000
χ464444-244-4-444-2-2-2-2-2-2-2-4-44-4000022-2-222-2-220000002000000000000000000000000000000000000
χ474444-2-4-444-4-4-2-2-222224-44-40000-2-2-2-22222-20000002000000000000000000000000000000000000
χ484444-2-4-4-4-444-2-2-222224-4-4400002222-2-2-2-2-20000002000000000000000000000000000000000000
χ4944-4-444-400004-4-444-4-400000000000000000000000000000000000000004-4000000000000000000
χ5044-4-444-400004-4-444-4-40000000000000000000000000000000000000000-44000000000000000000
χ5144-4-44-4400004-4-4-4-4440000000000000000000000000000000000000000004i−4i0000000000000000
χ5244-4-44-4400004-4-4-4-444000000000000000000000000000000000000000000−4i4i0000000000000000
χ534-44-4400004i−4i-44-40000000000000000004i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ544-44-4400004i−4i-44-40000000000000000004i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ554-44-440000−4i4i-44-4000000000000000000−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ564-44-440000−4i4i-44-4000000000000000000−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ574-44-4-200004i−4i2-2223−2323−230000000000−2i32i300−2i2i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000
χ584-44-4-200004i−4i2-2223−2323−230000000000−2i32i300−2i2i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000
χ594-44-4-200004i−4i2-22−2323−232300000000002i3−2i300−2i2i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000
χ604-44-4-200004i−4i2-22−2323−232300000000002i3−2i300−2i2i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000
χ614-44-4-20000−4i4i2-2223−2323−2300000000002i3−2i3002i−2i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000
χ624-44-4-20000−4i4i2-2223−2323−2300000000002i3−2i3002i−2i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000
χ634-44-4-20000−4i4i2-22−2323−23230000000000−2i32i3002i−2i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000
χ644-44-4-20000−4i4i2-22−2323−23230000000000−2i32i3002i−2i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000
χ654-4-444004i−4i00-4-44000000002+2i−2−2i2−2i−2+2i4i−4i000000000000002+2i−2−2i002−2i−2+2i000000000000000000000000000000
χ664-4-444004i−4i00-4-4400000000−2−2i2+2i−2+2i2−2i4i−4i00000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000000000
χ674-4-44400−4i4i00-4-44000000002−2i−2+2i2+2i−2−2i−4i4i000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000000000
χ684-4-44400−4i4i00-4-4400000000−2+2i2−2i−2−2i2+2i−4i4i00000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000000000
χ694-4-44-2004i−4i0022-223−23−232300002+2i−2−2i2−2i−2+2i−2i2i00−2i32i30000000000−1−i1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−1+i1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ704-4-44-2004i−4i0022-223−23−23230000−2−2i2+2i−2+2i2−2i−2i2i00−2i32i300000000001+i−1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ221−i−1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000
χ714-4-44-2004i−4i0022-2−232323−2300002+2i−2−2i2−2i−2+2i−2i2i002i3−2i30000000000−1−i1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−1+i1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000
χ724-4-44-2004i−4i0022-2−232323−230000−2−2i2+2i−2+2i2−2i−2i2i002i3−2i300000000001+i−1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221−i−1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ734-4-44-200−4i4i0022-223−23−232300002−2i−2+2i2+2i−2−2i2i−2i002i3−2i30000000000−1+i1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−1−i1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000
χ744-4-44-200−4i4i0022-223−23−23230000−2+2i2−2i−2−2i2+2i2i−2i002i3−2i300000000001−i−1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ221+i−1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ754-4-44-200−4i4i0022-2−232323−2300002−2i−2+2i2+2i−2−2i2i−2i00−2i32i30000000000−1+i1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−1−i1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ764-4-44-200−4i4i0022-2−232323−230000−2+2i2−2i−2−2i2+2i2i−2i00−2i32i300000000001−i−1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ221+i−1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000
χ7788-8-8-48-80000-444-4-444000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-4-880000-44444-4-4000000000000000000000000000000000000000000000000000000000000

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