Finite Group Databasebeta

← Group #10691034

Character table — Group #10691034

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446661212121244466888812121212121244448812121212121212121212242424242424242444444412121212448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ91111-1-11-1-111-1-1111-1-1-1-111-1-1-1ii−i−i1111-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-1-11ii−i−iii−i−i1-1
χ101111-1-11-1-111-1-1111-1-1-1-111-1-1-1ii−i−i1111-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-11-1−i−iii−i−iii-11
χ111111-1-11-1-111-1-1111-1-1-1-111-1-1-1ii−i−i1111-1-1−i−iiii−i1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-111-11ii−i−i−i−iii-11
χ121111-1-11-1-111-1-1111-1-1-1-111-1-1-1ii−i−i1111-1-1−i−iiii−i1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-1111-1−i−iiiii−i−i1-1
χ131111-1-11-1-111-1-1111-1-1-1-111-1-1-1−i−iii1111-1-1ii−i−i−ii1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-111-11−i−iiiii−i−i-11
χ141111-1-11-1-111-1-1111-1-1-1-111-1-1-1−i−iii1111-1-1ii−i−i−ii1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-1111-1ii−i−i−i−iii1-1
χ151111-1-11-1-111-1-1111-1-1-1-111-1-1-1−i−iii1111-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-1-11−i−iii−i−iii1-1
χ161111-1-11-1-111-1-1111-1-1-1-111-1-1-1−i−iii1111-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-11-1ii−i−iii−i−i-11
χ17222222222-2-2-2-22222222-22-222000022-2-2-2-2000000-2-200000000000000000000000000002i−2i2i−2i000000
χ18222222222-2-2-2-22222222-22-222000022-2-2-2-2000000-2-20000000000000000000000000000−2i2i−2i2i000000
χ192222222-2-222-2-2222-2-2-2-2-2-22220000-2-222-2-2000000-22000000000000000022-2-20000002-20000000000
χ202222222-2-222-2-2222-2-2-2-2-2-22220000-2-222-2-2000000-220000000000000000-2-222000000-220000000000
χ212222222-2-2-2-222222-2-2-2-22-2-2222222-2-2-2-2220000-2-22-20000000022-2-222-2-20000000000000000000000
χ222222222-2-2-2-222222-2-2-2-22-2-222-2-2-2-2-2-2-2-2220000222-200000000-2-222-2-2220000000000000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ26222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ27222222-1-2-2-2-222-1-1-111112-2-2-1-122221111-1-10000-2-2-11−i3−i3i3i3−i3−i3i3i3-1-111-1-111000000−i3i3−i3i3000000000000
χ28222222-1-2-2-2-222-1-1-111112-2-2-1-122221111-1-10000-2-2-11i3i3−i3−i3i3i3−i3−i3-1-111-1-111000000i3−i3i3−i3000000000000
χ29222222-1-2-2-2-222-1-1-111112-2-2-1-1-2-2-2-21111-1-1000022-11−i3−i3i3i3−i3−i3i3i311-1-111-1-1000000i3−i3i3−i3000000000000
χ30222222-1-2-2-2-222-1-1-111112-2-2-1-1-2-2-2-21111-1-1000022-11i3i3−i3−i3i3i3−i3−i311-1-111-1-1000000−i3i3−i3i3000000000000
χ312222-2-222222222222222-2-2-2-2-20000-2-22222000000-2-200000000000000002222000000-2-20000000000
χ322222-2-222222222222222-2-2-2-2-20000-2-22222000000-2-20000000000000000-2-2-2-2000000220000000000
χ332222-2-2222-2-2-2-222222222-22-2-22i2i−2i−2i-2-2-2-2-2-20000−2i2i22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ342222-2-2222-2-2-2-222222222-22-2-2−2i−2i2i2i-2-2-2-2-2-200002i−2i2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ352222-2-22-2-2-2-222222-2-2-2-2-222-2-2000022-2-222000000-2200000000000000000000000000002-2-22000000
χ362222-2-22-2-2-2-222222-2-2-2-2-222-2-2000022-2-222000000-220000000000000000000000000000-222-2000000
χ372222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-22112i2i−2i−2i1111110000−2i2i-1-133−3−3−3−333−i−iiiii−i−i000000−i3i3i3−i3000000000000
χ382222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-22112i2i−2i−2i1111110000−2i2i-1-1−3−33333−3−3−i−iiiii−i−i000000i3−i3−i3i3000000000000
χ392222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-2211−2i−2i2i2i11111100002i−2i-1-133−3−3−3−333ii−i−i−i−iii000000i3−i3−i3i3000000000000
χ402222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-2211−2i−2i2i2i11111100002i−2i-1-1−3−33333−3−3ii−i−i−i−iii000000−i3i3i3−i3000000000000
χ412222-2-2-1-2-222-2-2-1-1-1111122-2112i2i−2i−2i-1-1-1-1112i2i−2i−2i2i−2i-11−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ422222-2-2-1-2-222-2-2-1-1-1111122-2112i2i−2i−2i-1-1-1-111−2i−2i2i2i2i−2i-11iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ432222-2-2-1-2-222-2-2-1-1-1111122-211−2i−2i2i2i-1-1-1-1112i2i−2i−2i−2i2i-11−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ442222-2-2-1-2-222-2-2-1-1-1111122-211−2i−2i2i2i-1-1-1-111−2i−2i2i2i−2i2i-11iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ452-2-220022i−2i2-22i−2i-22-22i2i−2i−2i000000000002-22i−2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000002i−2i2-20000000000001+i−1−i1−i−1+i00
χ462-2-220022i−2i2-22i−2i-22-22i2i−2i−2i000000000002-22i−2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−2i2i-22000000000000−1−i1+i−1+i1−i00
χ472-2-220022i−2i2-22i−2i-22-22i2i−2i−2i000000000002-22i−2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000002i−2i2-2000000000000−1−i1+i−1+i1−i00
χ482-2-220022i−2i2-22i−2i-22-22i2i−2i−2i000000000002-22i−2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−2i2i-220000000000001+i−1−i1−i−1+i00
χ492-2-22002−2i2i2-2−2i2i-22-2−2i−2i2i2i000000000002-2−2i2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002i−2i-22000000000000−1+i1−i−1−i1+i00
χ502-2-22002−2i2i2-2−2i2i-22-2−2i−2i2i2i000000000002-2−2i2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−2i2i2-20000000000001−i−1+i1+i−1−i00
χ512-2-22002−2i2i2-2−2i2i-22-2−2i−2i2i2i000000000002-2−2i2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000002i−2i-220000000000001−i−1+i1+i−1−i00
χ522-2-22002−2i2i2-2−2i2i-22-2−2i−2i2i2i000000000002-2−2i2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−2i2i2-2000000000000−1+i1−i−1−i1+i00
χ53444444-244-4-4-4-4-2-2-2-2-2-2-2-44-4-2-20000-2-222220000002200000000000000000000000000000000000000
χ54444444-2-4-444-4-4-2-2-22222-4-44-2-2000022-2-2220000002-200000000000000000000000000000000000000
χ554444-4-4-2444444-2-2-2-2-2-2-2-4-4-422000022-2-2-2-20000002200000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-444-2-2-22222-444220000-2-222-2-20000002-200000000000000000000000000000000000000
χ574-44-44-440000004-4-400000004-422−2222−22000000000000000000000022−220022−22000000000000000000000000
χ584-44-44-440000004-4-400000004-4−2222−22220000000000000000000000−222200−2222000000000000000000000000
χ594-44-44-4-2000000-222−2i32i3−2i32i3000-2222−2222−22−2i32i300000000000000000000−22i6−i6−22i6−i60000000000000000000000
χ604-44-44-4-2000000-222−2i32i3−2i32i3000-22−2222−2222−2i32i3000000000000000000002−2−i6i62−2−i6i60000000000000000000000
χ614-44-44-4-2000000-2222i3−2i32i3−2i3000-2222−2222−222i3−2i300000000000000000000−22−i6i6−22−i6i60000000000000000000000
χ624-44-44-4-2000000-2222i3−2i32i3−2i3000-22−2222−22222i3−2i3000000000000000000002−2i6−i62−2i6−i60000000000000000000000
χ634-44-4-4440000004-4-40000000-44−2i22i22i2−2i20000000000000000000000−2i22i2002i2−2i2000000000000000000000000
χ644-44-4-4440000004-4-40000000-442i2−2i2−2i22i200000000000000000000002i2−2i200−2i22i2000000000000000000000000
χ654-44-4-44-2000000-222−2i32i3−2i32i30002-2−2i22i22i2−2i22i3−2i300000000000000000000i2−i2−66−i2i26−60000000000000000000000
χ664-44-4-44-2000000-222−2i32i3−2i32i30002-22i2−2i2−2i22i22i3−2i300000000000000000000−i2i26−6i2−i2−660000000000000000000000
χ674-44-4-44-2000000-2222i3−2i32i3−2i30002-2−2i22i22i2−2i2−2i32i300000000000000000000i2−i26−6−i2i2−660000000000000000000000
χ684-44-4-44-2000000-2222i3−2i32i3−2i30002-22i2−2i2−2i22i2−2i32i300000000000000000000−i2i2−66i2−i26−60000000000000000000000
χ694-4-440044i−4i-44−4i4i-44-44i4i−4i−4i00000000000-44−4i4i0000000000000000000000000000000000000000000000
χ704-4-44004−4i4i-444i−4i-44-4−4i−4i4i4i00000000000-444i−4i0000000000000000000000000000000000000000000000
χ714-4-4400-24i−4i4-44i−4i2-22−2i−2i2i2i00000000000-22−2i2i2−2i−2+2i2+2i−2−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000000000
χ724-4-4400-24i−4i4-44i−4i2-22−2i−2i2i2i00000000000-22−2i2i−2+2i2−2i−2−2i2+2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000000000
χ734-4-4400-24i−4i-44−4i4i2-22−2i−2i2i2i000000000002-22i−2i00000000−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−ζ22000000000000000000000000000000
χ744-4-4400-24i−4i-44−4i4i2-22−2i−2i2i2i000000000002-22i−2i00000000ζ4+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+ζ22000000000000000000000000000000
χ754-4-4400-2−4i4i4-4−4i4i2-222i2i−2i−2i00000000000-222i−2i2+2i−2−2i2−2i−2+2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000000000
χ764-4-4400-2−4i4i4-4−4i4i2-222i2i−2i−2i00000000000-222i−2i−2−2i2+2i−2+2i2−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000000000
χ774-4-4400-2−4i4i-444i−4i2-222i2i−2i−2i000000000002-2−2i2i00000000−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+ζ22000000000000000000000000000000
χ784-4-4400-2−4i4i-444i−4i2-222i2i−2i−2i000000000002-2−2i2i00000000ζ4−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−ζ22000000000000000000000000000000
χ7988-8-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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