Finite Group Databasebeta

← Group #128583

Character table — Group #128583

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222222222222444444444444448888888888888888888888888888888888881616161616161616
order1244222444888888888888444444448888882244444444888888888888888888888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ121111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ131111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ141111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ1711111-1-11-1-111-1-1111111-1-1ii−i−i11-1-1-1-1ii−i−i1-11-1i−iii−i−i11-1-1i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ1811111-1-11-1-111-1-1111111-1-1ii−i−i11-1-1-1-1ii−i−i1-11-1i−iii−i−i11-1-1i−iii−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ1911111-1-11-1-111-1-1111111-1-1ii−i−i11-1-1-1-1ii−i−i-11-11i−i−i−iii-1-111i−i−i−iii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ2011111-1-11-1-111-1-1111111-1-1ii−i−i11-1-1-1-1ii−i−i-11-11i−i−i−iii-1-111i−i−i−iii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ2111111-1-11-1-111-1-1111111-1-1−i−iii11-1-1-1-1−i−iii1-11-1−ii−i−iii11-1-1−ii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ2211111-1-11-1-111-1-1111111-1-1−i−iii11-1-1-1-1−i−iii1-11-1−ii−i−iii11-1-1−ii−i−iii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ2311111-1-11-1-111-1-1111111-1-1−i−iii11-1-1-1-1−i−iii-11-11−iiii−i−i-1-111−iiii−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ2411111-1-11-1-111-1-1111111-1-1−i−iii11-1-1-1-1−i−iii-11-11−iiii−i−i-1-111−iiii−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ2511111-1-11-1-1-1-1111111-1-111ii−i−i-1-111-1-1−i−iii1-11-1−iiii−i−i-1-111i−i−i−iiiii−i−i−i−iii-1-11111-1-1i−i−ii-111-1
χ2611111-1-11-1-1-1-1111111-1-111ii−i−i-1-111-1-1−i−iii1-11-1−iiii−i−i-1-111i−i−i−iii−i−iiiii−i−i11-1-1-1-111−iii−i1-1-11
χ2711111-1-11-1-1-1-1111111-1-111ii−i−i-1-111-1-1−i−iii-11-11−ii−i−iii11-1-1i−iii−i−iii−i−i−i−iii-1-11111-1-1−iii−i1-1-11
χ2811111-1-11-1-1-1-1111111-1-111ii−i−i-1-111-1-1−i−iii-11-11−ii−i−iii11-1-1i−iii−i−i−i−iiiii−i−i11-1-1-1-111i−i−ii-111-1
χ2911111-1-11-1-1-1-1111111-1-111−i−iii-1-111-1-1ii−i−i1-11-1i−i−i−iii-1-111−iiii−i−iii−i−i−i−iii11-1-1-1-111i−i−ii1-1-11
χ3011111-1-11-1-1-1-1111111-1-111−i−iii-1-111-1-1ii−i−i1-11-1i−i−i−iii-1-111−iiii−i−i−i−iiiii−i−i-1-11111-1-1−iii−i-111-1
χ3111111-1-11-1-1-1-1111111-1-111−i−iii-1-111-1-1ii−i−i-11-11i−iii−i−i11-1-1−ii−i−iiiii−i−i−i−iii11-1-1-1-111−iii−i-111-1
χ3211111-1-11-1-1-1-1111111-1-111−i−iii-1-111-1-1ii−i−i-11-11i−iii−i−i11-1-1−ii−i−iii−i−iiiii−i−i-1-11111-1-1i−i−ii1-1-11
χ3322222222222222-2-2-2-222222222-2-2-2-2-2-222220000-2-200000000-2-20000000000000000000000000000
χ3422222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-200002200000000220000000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-200002200000000-2-20000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222220000-2-200000000220000000000000000000000000000
χ3722222-2-22-2-222-2-2-2-2-2-222-2-22i2i−2i−2i-2-222222i2i−2i−2i0000−2i2i00000000−2i2i0000000000000000000000000000
χ3822222-2-22-2-222-2-2-2-2-2-222-2-2−2i−2i2i2i-2-22222−2i−2i2i2i00002i−2i000000002i−2i0000000000000000000000000000
χ3922222-2-22-2-2-2-222-2-2-2-2-2-2222i2i−2i−2i22-2-222−2i−2i2i2i00002i−2i00000000−2i2i0000000000000000000000000000
χ4022222-2-22-2-2-2-222-2-2-2-2-2-222−2i−2i2i2i22-2-2222i2i−2i−2i0000−2i2i000000002i−2i0000000000000000000000000000
χ412222-22-2-22-222-2-20000-2-2222i−2i2i−2i0000002i−2i2i−2i00000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ422222-22-2-22-222-2-20000-2-2222i−2i2i−2i0000002i−2i2i−2i00000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ432222-22-2-22-222-2-20000-2-222−2i2i−2i2i000000−2i2i−2i2i00000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ442222-22-2-22-222-2-20000-2-222−2i2i−2i2i000000−2i2i−2i2i00000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ452222-22-2-22-2-2-222000022-2-22i−2i2i−2i000000−2i2i−2i2i000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ462222-22-2-22-2-2-222000022-2-22i−2i2i−2i000000−2i2i−2i2i00000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ472222-22-2-22-2-2-222000022-2-2−2i2i−2i2i0000002i−2i2i−2i000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ482222-22-2-22-2-2-222000022-2-2−2i2i−2i2i0000002i−2i2i−2i00000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ492222-2-22-2-2222220000-2-2-2-22-2-220000002-2-2200000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ502222-2-22-2-2222220000-2-2-2-22-2-220000002-2-2200000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ512222-2-22-2-2222220000-2-2-2-2-222-2000000-222-200000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ522222-2-22-2-2222220000-2-2-2-2-222-2000000-222-200000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ532222-2-22-2-22-2-2-2-2000022222-2-22000000-222-2000000000000000000002−2−22−222−2−222−22−2−2200000000
χ542222-2-22-2-22-2-2-2-2000022222-2-22000000-222-200000000000000000000−222−22−2−222−2−22−222−200000000
χ552222-2-22-2-22-2-2-2-200002222-222-20000002-2-22000000000000000000002−2−22−222−22−2−22−222−200000000
χ562222-2-22-2-22-2-2-2-200002222-222-20000002-2-2200000000000000000000−222−22−2−22−222−22−2−2200000000
χ5722-2-2-22-22-222i−2i2i−2i22-2-22i−2i2i−2i00002i−2i2i−2i2-200000000002i−2i2i−2i0000002-22-2000000000000000000000000
χ5822-2-2-22-22-222i−2i2i−2i22-2-22i−2i2i−2i00002i−2i2i−2i2-20000000000−2i2i−2i2i000000-22-22000000000000000000000000
χ5922-2-2-22-22-222i−2i2i−2i-2-2222i−2i2i−2i0000−2i2i−2i2i-2200002-2-220000002i−2i2i−2i000000000000000000000000000000
χ6022-2-2-22-22-222i−2i2i−2i-2-2222i−2i2i−2i0000−2i2i−2i2i-220000-222-2000000−2i2i−2i2i000000000000000000000000000000
χ6122-2-2-22-22-22−2i2i−2i2i22-2-2−2i2i−2i2i0000−2i2i−2i2i2-200000000002i−2i2i−2i000000-22-22000000000000000000000000
χ6222-2-2-22-22-22−2i2i−2i2i22-2-2−2i2i−2i2i0000−2i2i−2i2i2-20000000000−2i2i−2i2i0000002-22-2000000000000000000000000
χ6322-2-2-22-22-22−2i2i−2i2i-2-222−2i2i−2i2i00002i−2i2i−2i-2200002-2-22000000−2i2i−2i2i000000000000000000000000000000
χ6422-2-2-22-22-22−2i2i−2i2i-2-222−2i2i−2i2i00002i−2i2i−2i-220000-222-20000002i−2i2i−2i000000000000000000000000000000
χ6522-2-2-2-2222-22i−2i−2i2i22-2-22i−2i−2i2i00002i−2i−2i2i-2200000000002-2-22000000−2i2i2i−2i000000000000000000000000
χ6622-2-2-2-2222-22i−2i−2i2i22-2-22i−2i−2i2i00002i−2i−2i2i-220000000000-222-20000002i−2i−2i2i000000000000000000000000
χ6722-2-2-2-2222-22i−2i−2i2i-2-2222i−2i−2i2i0000−2i2i2i−2i2-2000022-2-20000002i−2i−2i2i000000000000000000000000000000
χ6822-2-2-2-2222-22i−2i−2i2i-2-2222i−2i−2i2i0000−2i2i2i−2i2-20000-2-222000000−2i2i2i−2i000000000000000000000000000000
χ6922-2-2-2-2222-2−2i2i2i−2i22-2-2−2i2i2i−2i0000−2i2i2i−2i-2200000000002-2-220000002i−2i−2i2i000000000000000000000000
χ7022-2-2-2-2222-2−2i2i2i−2i22-2-2−2i2i2i−2i0000−2i2i2i−2i-220000000000-222-2000000−2i2i2i−2i000000000000000000000000
χ7122-2-2-2-2222-2−2i2i2i−2i-2-222−2i2i2i−2i00002i−2i−2i2i2-2000022-2-2000000−2i2i2i−2i000000000000000000000000000000
χ7222-2-2-2-2222-2−2i2i2i−2i-2-222−2i2i2i−2i00002i−2i−2i2i2-20000-2-2220000002i−2i−2i2i000000000000000000000000000000
χ7344-4-4444-4-4-44i−4i−4i4i0000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ7444-4-4444-4-4-4−4i4i4i−4i00004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-4-4444i−4i4i−4i0000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ7644-4-44-4-4-444−4i4i−4i4i00004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ778-88i−8i00000000004i2−4i242−4200000000000000000000000000000000000000000000000000000000000000
χ788-88i−8i0000000000−4i24i2−424200000000000000000000000000000000000000000000000000000000000000
χ798-8−8i8i00000000004i2−4i2−424200000000000000000000000000000000000000000000000000000000000000
χ808-8−8i8i0000000000−4i24i242−4200000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).