Finite Group Databasebeta

← Group #230158

Character table — Group #230158

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888844444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1111111-1-111-1-1-1-1
χ91111111111111111-1-1-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ17111-1-1-1-11-11-1-1-111111-1-1ii−i−iii−i−i1-1ii−i−i11-1-111-1-1i−ii−ii−ii−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−ii−i1-11-1
χ18111-1-1-1-11-11-1-1-111111-1-1ii−i−iii−i−i1-1ii−i−i-1-111-1-111i−i−iii−i−ii1-1i−i11-1-1−i−iii-1-111−i−iii1-1i−i−ii-11-11
χ19111-1-1-1-11-11-1-1-111111-1-1ii−i−i−i−iii1-1ii−i−i11-1-111-1-1i−i−ii−ii−ii1-1i−i-1-111ii−i−i11-1-1ii−i−i-11−ii−ii-11-11
χ20111-1-1-1-11-11-1-1-111111-1-1ii−i−i−i−iii1-1ii−i−i-1-111-1-111i−ii−i−iii−i1-1i−i-1-111−i−iii-1-111−i−iii-11−iii−i1-11-1
χ21111-1-1-1-11-11-1-1-111111-1-1−i−iiiii−i−i1-1−i−iii11-1-111-1-1−iii−ii−ii−i1-1−ii-1-111−i−iii11-1-1−i−iii-11i−ii−i-11-11
χ22111-1-1-1-11-11-1-1-111111-1-1−i−iiiii−i−i1-1−i−iii-1-111-1-111−ii−iii−i−ii1-1−ii-1-111ii−i−i-1-111ii−i−i-11i−i−ii1-11-1
χ23111-1-1-1-11-11-1-1-111111-1-1−i−iii−i−iii1-1−i−iii11-1-111-1-1−ii−ii−ii−ii1-1−ii11-1-1−i−iii11-1-1−i−iii1-1−ii−ii1-11-1
χ24111-1-1-1-11-11-1-1-111111-1-1−i−iii−i−iii1-1−i−iii-1-111-1-111−iii−i−iii−i1-1−ii11-1-1ii−i−i-1-111ii−i−i1-1−iii−i-11-11
χ25111-1-1-1-11-11-1-1-1111-1-111ii−i−iii−i−i1-1−i−iii11-1-111-1-1i−ii−ii−ii−i-11−ii-1-111ii−i−i-1-111−i−iii1-1−ii−ii1-1-11
χ26111-1-1-1-11-11-1-1-1111-1-111ii−i−iii−i−i1-1−i−iii-1-111-1-111i−i−iii−i−ii-11−ii-1-111−i−iii11-1-1ii−i−i1-1−iii−i-111-1
χ27111-1-1-1-11-11-1-1-1111-1-111ii−i−i−i−iii1-1−i−iii11-1-111-1-1i−i−ii−ii−ii-11−ii11-1-1ii−i−i-1-111−i−iii-11i−ii−i-111-1
χ28111-1-1-1-11-11-1-1-1111-1-111ii−i−i−i−iii1-1−i−iii-1-111-1-111i−ii−i−iii−i-11−ii11-1-1−i−iii11-1-1ii−i−i-11i−i−ii1-1-11
χ29111-1-1-1-11-11-1-1-1111-1-111−i−iiiii−i−i1-1ii−i−i11-1-111-1-1−iii−ii−ii−i-11i−i11-1-1−i−iii-1-111ii−i−i-11−ii−ii-111-1
χ30111-1-1-1-11-11-1-1-1111-1-111−i−iiiii−i−i1-1ii−i−i-1-111-1-111−ii−iii−i−ii-11i−i11-1-1ii−i−i11-1-1−i−iii-11−iii−i1-1-11
χ31111-1-1-1-11-11-1-1-1111-1-111−i−iii−i−iii1-1ii−i−i11-1-111-1-1−ii−ii−ii−ii-11i−i-1-111−i−iii-1-111ii−i−i1-1i−ii−i1-1-11
χ32111-1-1-1-11-11-1-1-1111-1-111−i−iii−i−iii1-1ii−i−i-1-111-1-111−iii−i−iii−i-11i−i-1-111ii−i−i11-1-1−i−iii1-1i−i−ii-111-1
χ332222222222-2-22-2-22000000002222-2-200002222-2-2-2-20022-2-2-2-2000000000000000000000000000000
χ342222222222-2-22-2-22000000002222-2-20000-2-2-2-2222200-2-2-2-222000000000000000000000000000000
χ352222222222-2-22-2-2200000000-2-2-2-2-2-200002222-2-2-2-200-2-22222000000000000000000000000000000
χ362222222222-2-22-2-2200000000-2-2-2-2-2-20000-2-2-2-22222002222-2-2000000000000000000000000000000
χ3722222222-2-222-222-2222222220000-2-2222200000000-2-2000000-2-2-2-200000000000000000000000000
χ3822222222-2-222-222-22222-2-2-2-20000-2-2-2-2-2-20000000022000000-2-22200000000000000000000000000
χ3922222222-2-222-222-2-2-2-2-222220000-2-2-2-2-2-200000000-2-2000000222200000000000000000000000000
χ4022222222-2-222-222-2-2-2-2-2-2-2-2-20000-2-22222000000002200000022-2-200000000000000000000000000
χ41222-2-2-2-222-2-2-2222-222-2-22i2i−2i−2i0000-222i2i−2i−2i00000000−2i2i000000-22−2i2i00000000000000000000000000
χ42222-2-2-2-222-2-2-2222-222-2-2−2i−2i2i2i0000-22−2i−2i2i2i000000002i−2i000000-222i−2i00000000000000000000000000
χ43222-2-2-2-222-2-2-2222-2-2-2222i2i−2i−2i0000-22−2i−2i2i2i00000000−2i2i0000002-22i−2i00000000000000000000000000
χ44222-2-2-2-222-2-2-2222-2-2-222−2i−2i2i2i0000-222i2i−2i−2i000000002i−2i0000002-2−2i2i00000000000000000000000000
χ45222-2-2-2-22-2222-2-2-22000000002i2i−2i−2i-22000022-2-2-2-222002i−2i−2i2i−2i2i000000000000000000000000000000
χ46222-2-2-2-22-2222-2-2-22000000002i2i−2i−2i-220000-2-22222-2-200−2i2i−2i2i2i−2i000000000000000000000000000000
χ47222-2-2-2-22-2222-2-2-2200000000−2i−2i2i2i-22000022-2-2-2-22200−2i2i2i−2i2i−2i000000000000000000000000000000
χ48222-2-2-2-22-2222-2-2-2200000000−2i−2i2i2i-220000-2-22222-2-2002i−2i2i−2i−2i2i000000000000000000000000000000
χ492-222-22-2-2002-202-202-22-22-22-20000002-22-2i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ502-222-22-2-2002-202-202-22-22-22-20000002-22-2−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ512-222-22-2-2002-202-202-22-2-22-22000000-22-22i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ522-222-22-2-2002-202-202-22-2-22-22000000-22-22−i2i2−i2i2−i2i2−i2i20000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ532-222-22-2-2002-202-20-22-222-22-2000000-22-22i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ542-222-22-2-2002-202-20-22-222-22-2000000-22-22−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ552-222-22-2-2002-202-20-22-22-22-220000002-22-2i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ562-222-22-2-2002-202-20-22-22-22-220000002-22-2−i2i2−i2i2−i2i2−i2i20000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ572-22-22-22-200-2202-202-2-222i−2i−2i2i0000002i−2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000−222−2i2−i2−i2i2−222−20000000000
χ582-22-22-22-200-2202-202-2-222i−2i−2i2i0000002i−2i−2i2i−i2i2i2−i2−i2i2i2−i200000000000000002−2−22−i2i2i2−i22−2−220000000000
χ592-22-22-22-200-2202-202-2-22−2i2i2i−2i000000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i200000000000000002−2−22i2−i2−i2i22−2−220000000000
χ602-22-22-22-200-2202-202-2-22−2i2i2i−2i000000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000−222−2−i2i2i2−i2−222−20000000000
χ612-22-22-22-200-2202-20-222-22i−2i−2i2i000000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000−222−2−i2i2i2−i22−2−220000000000
χ622-22-22-22-200-2202-20-222-22i−2i−2i2i000000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i200000000000000002−2−22i2−i2−i2i2−222−20000000000
χ632-22-22-22-200-2202-20-222-2−2i2i2i−2i0000002i−2i−2i2ii2−i2−i2i2i2−i2−i2i200000000000000002−2−22−i2i2i2−i2−222−20000000000
χ642-22-22-22-200-2202-20-222-2−2i2i2i−2i0000002i−2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000−222−2i2−i2−i2i22−2−220000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ66444-4-4-4-444-4444-4-4-40000000000004-400000000000000000000000000000000000000000000000000
χ6744-444-4-4-44400-400-4000000004-44-40000000000000000000000000000000000000000000000000000
χ6844-444-4-4-44400-400-400000000-44-440000000000000000000000000000000000000000000000000000
χ6944-444-4-4-4-4-4004004000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ7044-444-4-4-4-4-400400400000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ7144-4-4-444-44-400-4004000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ7244-4-4-444-44-400-400400000000000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ7344-4-4-444-4-4400400-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ7444-4-4-444-4-4400400-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ754-444-44-4-400-440-4400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ764-444-44-4-400-440-440000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ774-44-44-44-4004-40-4400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ784-44-44-44-4004-40-440000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ798-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000

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