Finite Group Databasebeta

← Group #230120

Character table — Group #230120

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444442222444444444488888888888844444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ31111111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111
χ7111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-111111111-1-1-1-1-1-1
χ91111111111111111-1-1-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-11-1-1-1-11111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1
χ151111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111
χ17111-1-1-11-1-1-1-1111-1111-1-11ii−i−iii−i−i-1ii−i−i11-1-111-1-1i−ii−ii−ii−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1
χ18111-1-1-11-1-1-1-1111-1111-1-11ii−i−iii−i−i-1ii−i−i-1-111-1-111i−ii−i−ii−ii1-1i−i11-1-1−i−iii-1-111−i−iii1-1−ii-11i−i-11
χ19111-1-1-11-1-1-1-1111-1111-1-11ii−i−i−i−iii-1ii−i−i11-1-111-1-1−iii−i−ii−ii1-1i−i-1-111ii−i−i11-1-1ii−i−i-11−ii-11−ii-11
χ20111-1-1-11-1-1-1-1111-1111-1-11ii−i−i−i−iii-1ii−i−i-1-111-1-111−iii−ii−ii−i1-1i−i-1-111−i−iii-1-111−i−iii-11i−i1-1−ii1-1
χ21111-1-1-11-1-1-1-1111-1111-1-11−i−iiiii−i−i-1−i−iii11-1-111-1-1i−i−iii−ii−i1-1−ii-1-111−i−iii11-1-1−i−iii-11i−i-11i−i-11
χ22111-1-1-11-1-1-1-1111-1111-1-11−i−iiiii−i−i-1−i−iii-1-111-1-111i−i−ii−ii−ii1-1−ii-1-111ii−i−i-1-111ii−i−i-11−ii1-1i−i1-1
χ23111-1-1-11-1-1-1-1111-1111-1-11−i−iii−i−iii-1−i−iii11-1-111-1-1−ii−ii−ii−ii1-1−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1
χ24111-1-1-11-1-1-1-1111-1111-1-11−i−iii−i−iii-1−i−iii-1-111-1-111−ii−iii−ii−i1-1−ii11-1-1ii−i−i-1-111ii−i−i1-1i−i-11−ii-11
χ25111-1-1-11-1-1-1-1111-11-1-1111ii−i−iii−i−i-1−i−iii11-1-111-1-1i−ii−ii−ii−i-11−ii-1-111ii−i−i-1-111−i−iii1-1−ii1-1−ii-11
χ26111-1-1-11-1-1-1-1111-11-1-1111ii−i−iii−i−i-1−i−iii-1-111-1-111i−ii−i−ii−ii-11−ii-1-111−i−iii11-1-1ii−i−i1-1i−i-11−ii1-1
χ27111-1-1-11-1-1-1-1111-11-1-1111ii−i−i−i−iii-1−i−iii11-1-111-1-1−iii−i−ii−ii-11−ii11-1-1ii−i−i-1-111−i−iii-11i−i-11i−i1-1
χ28111-1-1-11-1-1-1-1111-11-1-1111ii−i−i−i−iii-1−i−iii-1-111-1-111−iii−ii−ii−i-11−ii11-1-1−i−iii11-1-1ii−i−i-11−ii1-1i−i-11
χ29111-1-1-11-1-1-1-1111-11-1-1111−i−iiiii−i−i-1ii−i−i11-1-111-1-1i−i−iii−ii−i-11i−i11-1-1−i−iii-1-111ii−i−i-11−ii-11−ii1-1
χ30111-1-1-11-1-1-1-1111-11-1-1111−i−iiiii−i−i-1ii−i−i-1-111-1-111i−i−ii−ii−ii-11i−i11-1-1ii−i−i11-1-1−i−iii-11i−i1-1−ii-11
χ31111-1-1-11-1-1-1-1111-11-1-1111−i−iii−i−iii-1ii−i−i11-1-111-1-1−ii−ii−ii−ii-11i−i-1-111−i−iii-1-111ii−i−i1-1i−i1-1i−i-11
χ32111-1-1-11-1-1-1-1111-11-1-1111−i−iii−i−iii-1ii−i−i-1-111-1-111−ii−iii−ii−i-11i−i-1-111ii−i−i11-1-1−i−iii1-1−ii-11i−i1-1
χ33222222222-2-22-2-2220000-200002222-200002222-2-2-2-2-2-20022-2-2000000000000000000000000000000
χ34222222222-2-22-2-2220000-200002222-20000-2-2-2-22222-2-200-2-222000000000000000000000000000000
χ35222222222-2-22-2-2220000-20000-2-2-2-2-200002222-2-2-2-22200-2-222000000000000000000000000000000
χ36222222222-2-22-2-2220000-20000-2-2-2-2-20000-2-2-2-22222220022-2-2000000000000000000000000000000
χ3722222222-222-222-2-22222-222220000-222220000000000-2-20000-2-2-2-200000000000000000000000000
χ3822222222-222-222-2-22222-2-2-2-2-20000-2-2-2-2-20000000000220000-2-22200000000000000000000000000
χ3922222222-222-222-2-2-2-2-2-2-222220000-2-2-2-2-20000000000-2-20000222200000000000000000000000000
χ4022222222-222-222-2-2-2-2-2-2-2-2-2-2-20000-22222000000000022000022-2-200000000000000000000000000
χ41222-2-2-22-22-2-2-2222-222-2-2-22i2i−2i−2i000022i2i−2i−2i0000000000−2i2i0000-22−2i2i00000000000000000000000000
χ42222-2-2-22-22-2-2-2222-222-2-2-2−2i−2i2i2i00002−2i−2i2i2i00000000002i−2i0000-222i−2i00000000000000000000000000
χ43222-2-2-22-22-2-2-2222-2-2-222-22i2i−2i−2i00002−2i−2i2i2i0000000000−2i2i00002-22i−2i00000000000000000000000000
χ44222-2-2-22-22-2-2-2222-2-2-222-2−2i−2i2i2i000022i2i−2i−2i00000000002i−2i00002-2−2i2i00000000000000000000000000
χ45222-2-2-22-2-2222-2-2-220000-200002i2i−2i−2i2000022-2-2-2-222−2i2i002i−2i−2i2i000000000000000000000000000000
χ46222-2-2-22-2-2222-2-2-220000-200002i2i−2i−2i20000-2-22222-2-2−2i2i00−2i2i2i−2i000000000000000000000000000000
χ47222-2-2-22-2-2222-2-2-220000-20000−2i−2i2i2i2000022-2-2-2-2222i−2i00−2i2i2i−2i000000000000000000000000000000
χ48222-2-2-22-2-2222-2-2-220000-20000−2i−2i2i2i20000-2-22222-2-22i−2i002i−2i−2i2i000000000000000000000000000000
χ4922-22-2-2-2202-202-2002-22-202-22-2000002-22-2i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ5022-22-2-2-2202-202-2002-22-202-22-2000002-22-2−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ5122-22-2-2-2202-202-2002-22-20-22-2200000-22-22i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ5222-22-2-2-2202-202-2002-22-20-22-2200000-22-22−i2i2−i2i2−i2i2−i2i20000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ5322-22-2-2-2202-202-200-22-2202-22-200000-22-22i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ5422-22-2-2-2202-202-200-22-2202-22-200000-22-22−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ5522-22-2-2-2202-202-200-22-220-22-22000002-22-2i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ5622-22-2-2-2202-202-200-22-220-22-22000002-22-2−i2i2−i2i2−i2i2−i2i20000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ5722-2-222-2-20-2202-2002-2-2202i−2i−2i2i000002i−2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000−222−2i2−i2−i2i2−222−20000000000
χ5822-2-222-2-20-2202-2002-2-2202i−2i−2i2i000002i−2i−2i2i−i2i2i2−i2−i2i2i2−i200000000000000002−2−22−i2i2i2−i22−2−220000000000
χ5922-2-222-2-20-2202-2002-2-220−2i2i2i−2i00000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i200000000000000002−2−22i2−i2−i2i22−2−220000000000
χ6022-2-222-2-20-2202-2002-2-220−2i2i2i−2i00000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000−222−2−i2i2i2−i2−222−20000000000
χ6122-2-222-2-20-2202-200-222-202i−2i−2i2i00000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000−222−2−i2i2i2−i22−2−220000000000
χ6222-2-222-2-20-2202-200-222-202i−2i−2i2i00000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i200000000000000002−2−22i2−i2−i2i2−222−20000000000
χ6322-2-222-2-20-2202-200-222-20−2i2i2i−2i000002i−2i−2i2ii2−i2−i2i2i2−i2−i2i200000000000000002−2−22−i2i2i2−i2−222−20000000000
χ6422-2-222-2-20-2202-200-222-20−2i2i2i−2i000002i−2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000−222−2i2−i2−i2i22−2−220000000000
χ6544444444-4-4-4-4-4-4-4-40000400000000400000000000000000000000000000000000000000000000000
χ66444-4-4-44-4444-4-4-44-40000400000000-400000000000000000000000000000000000000000000000000
χ6744-44-4-4-440-440-44000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ6844-44-4-4-440-440-4400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ6944-4-444-4-404-40-44000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ7044-4-444-4-404-40-4400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ714-4-44-444-4400400-4-40000000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ724-4-44-444-4400400-4-4000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ734-4-44-444-4-400-400440000000000000000000000000000000000000022−2222−220000000000000000000000
χ744-4-44-444-4-400-4004400000000000000000000000000000000000000−2222−22220000000000000000000000
χ754-4-4-44-444400-400-440000000000000000000000000000000000000022−22−22220000000000000000000000
χ764-4-4-44-444400-400-4400000000000000000000000000000000000000−222222−220000000000000000000000
χ774-4-4-44-444-4004004-40000000004-4-44000000000000000000000000000000000000000000000000000
χ784-4-4-44-444-4004004-4000000000-444-4000000000000000000000000000000000000000000000000000
χ798-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000

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