Finite Group Databasebeta

← Group #229339

Character table — Group #229339

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888822444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ511111111111111111111-1-1-1-1111111111111111111-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111
χ111111111111111111-1-1-1-111111-1-1-1-111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1111111-1-1-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ171-11-1-111-1-111-1-1-111ii−i−iii−i−i1ii−i−i-1iiii−i−i−i−i11-1-11-11-1i−ii−ii−i1-1ii−i−i11-1-111-1-1ii−i−i1-11-1i−ii−i1-1
χ181-11-1-111-1-111-1-1-111ii−i−iii−i−i1ii−i−i-1−i−i−i−iiiii11-1-1-11-11i−ii−ii−i1-1ii−i−i-1-111-1-111−i−iii1-11-1−ii−ii-11
χ191-11-1-111-1-111-1-1-111ii−i−iii−i−i1−i−iii-1iiii−i−i−i−i-1-1111-11-1i−ii−i−ii-11−i−iii11-1-1-1-111−i−iii1-1-11i−i−ii-11
χ201-11-1-111-1-111-1-1-111ii−i−iii−i−i1−i−iii-1−i−i−i−iiiii-1-111-11-11i−ii−i−ii-11−i−iii-1-11111-1-1ii−i−i1-1-11−iii−i1-1
χ211-11-1-111-1-111-1-1-111ii−i−i−i−iii1ii−i−i-1iiii−i−i−i−i11-1-1-11-11i−i−iii−i1-1−i−iii11-1-111-1-1ii−i−i-11-11−ii−ii-11
χ221-11-1-111-1-111-1-1-111ii−i−i−i−iii1ii−i−i-1−i−i−i−iiiii11-1-11-11-1i−i−iii−i1-1−i−iii-1-111-1-111−i−iii-11-11i−ii−i1-1
χ231-11-1-111-1-111-1-1-111ii−i−i−i−iii1−i−iii-1iiii−i−i−i−i-1-111-11-11i−i−ii−ii-11ii−i−i11-1-1-1-111−i−iii-111-1−iii−i1-1
χ241-11-1-111-1-111-1-1-111ii−i−i−i−iii1−i−iii-1−i−i−i−iiiii-1-1111-11-1i−i−ii−ii-11ii−i−i-1-11111-1-1ii−i−i-111-1i−i−ii-11
χ251-11-1-111-1-111-1-1-111−i−iiiii−i−i1ii−i−i-1iiii−i−i−i−i-1-1111-11-1−iii−ii−i-11−i−iii-1-11111-1-1−i−iii-111-1−iii−i-11
χ261-11-1-111-1-111-1-1-111−i−iiiii−i−i1ii−i−i-1−i−i−i−iiiii-1-111-11-11−iii−ii−i-11−i−iii11-1-1-1-111ii−i−i-111-1i−i−ii1-1
χ271-11-1-111-1-111-1-1-111−i−iiiii−i−i1−i−iii-1iiii−i−i−i−i11-1-11-11-1−iii−i−ii1-1ii−i−i-1-111-1-111ii−i−i-11-11−ii−ii1-1
χ281-11-1-111-1-111-1-1-111−i−iiiii−i−i1−i−iii-1−i−i−i−iiiii11-1-1-11-11−iii−i−ii1-1ii−i−i11-1-111-1-1−i−iii-11-11i−ii−i-11
χ291-11-1-111-1-111-1-1-111−i−iii−i−iii1ii−i−i-1iiii−i−i−i−i-1-111-11-11−ii−iii−i-11ii−i−i-1-11111-1-1−i−iii1-1-11i−i−ii1-1
χ301-11-1-111-1-111-1-1-111−i−iii−i−iii1ii−i−i-1−i−i−i−iiiii-1-1111-11-1−ii−iii−i-11ii−i−i11-1-1-1-111ii−i−i1-1-11−iii−i-11
χ311-11-1-111-1-111-1-1-111−i−iii−i−iii1−i−iii-1iiii−i−i−i−i11-1-1-11-11−ii−ii−ii1-1−i−iii-1-111-1-111ii−i−i1-11-1i−ii−i-11
χ321-11-1-111-1-111-1-1-111−i−iii−i−iii1−i−iii-1−i−i−i−iiiii11-1-11-11-1−ii−ii−ii1-1−i−iii11-1-111-1-1−i−iii1-11-1−ii−ii1-1
χ33222222222-22-2-222-222220000-22222-20000000022220000-2-200-2-2-2-200000000000000000000000000
χ34222222222-22-2-222-222220000-2-2-2-2-2-200000000-2-2-2-20000-2-200222200000000000000000000000000
χ35222222222-22-2-222-2-2-2-2-20000-22222-200000000-2-2-2-200002200-2-22200000000000000000000000000
χ36222222222-22-2-222-2-2-2-2-20000-2-2-2-2-2-20000000022220000220022-2-200000000000000000000000000
χ3722222222-22-222-2-2200002222-20000-222-2-222-2-2000022-2-200-2-2000000000000000000000000000000
χ3822222222-22-222-2-2200002222-20000-2-2-222-2-2220000-2-22200-2-2000000000000000000000000000000
χ3922222222-22-222-2-220000-2-2-2-2-20000-222-2-222-2-20000-2-2220022000000000000000000000000000000
χ4022222222-22-222-2-220000-2-2-2-2-20000-2-2-222-2-222000022-2-20022000000000000000000000000000000
χ41222-2-2-2-2220-200-2202-22-2000002-22-20i2−i2i2−i2i2−i2i2−i22-22-20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ42222-2-2-2-2220-200-2202-22-2000002-22-20−i2i2−i2i2−i2i2−i2i22-22-20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ43222-2-2-2-2220-200-2202-22-200000-22-220i2−i2i2−i2i2−i2i2−i2-22-220000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ44222-2-2-2-2220-200-2202-22-200000-22-220−i2i2−i2i2−i2i2−i2i2-22-220000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ45222-2-2-2-2220-200-220-22-22000002-22-20i2−i2i2−i2i2−i2i2−i2-22-220000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ46222-2-2-2-2220-200-220-22-22000002-22-20−i2i2−i2i2−i2i2−i2i2-22-220000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ47222-2-2-2-2220-200-220-22-2200000-22-220i2−i2i2−i2i2−i2i2−i22-22-20000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ48222-2-2-2-2220-200-220-22-2200000-22-220−i2i2−i2i2−i2i2−i2i22-22-20000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ492-2222-2-2-2-20-2002202i−2i−2i2i000002i−2i−2i2i02−22−2−22−222-2-220000000000000000−i2i2i2−i2−i2i2i2−i22−2−220000000000
χ502-2222-2-2-2-20-2002202i−2i−2i2i000002i−2i−2i2i0−22−222−22−22-2-220000000000000000i2−i2−i2i2i2−i2−i2i2−222−20000000000
χ512-2222-2-2-2-20-2002202i−2i−2i2i00000−2i2i2i−2i02−22−2−22−22-222-20000000000000000−i2i2i2−i2i2−i2−i2i2−222−20000000000
χ522-2222-2-2-2-20-2002202i−2i−2i2i00000−2i2i2i−2i0−22−222−22−2-222-20000000000000000i2−i2−i2i2−i2i2i2−i22−2−220000000000
χ532-2222-2-2-2-20-200220−2i2i2i−2i000002i−2i−2i2i02−22−2−22−22-222-20000000000000000i2−i2−i2i2−i2i2i2−i2−222−20000000000
χ542-2222-2-2-2-20-200220−2i2i2i−2i000002i−2i−2i2i0−22−222−22−2-222-20000000000000000−i2i2i2−i2i2−i2−i2i22−2−220000000000
χ552-2222-2-2-2-20-200220−2i2i2i−2i00000−2i2i2i−2i02−22−2−22−222-2-220000000000000000i2−i2−i2i2i2−i2−i2i22−2−220000000000
χ562-2222-2-2-2-20-200220−2i2i2i−2i00000−2i2i2i−2i0−22−222−22−22-2-220000000000000000−i2i2i2−i2−i2i2i2−i2−222−20000000000
χ572-22-2-222-222-2-2-22-2200002i2i−2i−2i-2000022i2i−2i−2i−2i−2i2i2i00002-2-2200−2i2i000000000000000000000000000000
χ582-22-2-222-222-2-2-22-2200002i2i−2i−2i-200002−2i−2i2i2i2i2i−2i−2i0000-222-200−2i2i000000000000000000000000000000
χ592-22-2-222-222-2-2-22-220000−2i−2i2i2i-2000022i2i−2i−2i−2i−2i2i2i0000-222-2002i−2i000000000000000000000000000000
χ602-22-2-222-222-2-2-22-220000−2i−2i2i2i-200002−2i−2i2i2i2i2i−2i−2i00002-2-22002i−2i000000000000000000000000000000
χ612-22-2-222-2-2-2222-22-22i2i−2i−2i0000-22i2i−2i−2i20000000022-2-20000−2i2i00−2i2i-2200000000000000000000000000
χ622-22-2-222-2-2-2222-22-22i2i−2i−2i0000-2−2i−2i2i2i200000000-2-2220000−2i2i002i−2i2-200000000000000000000000000
χ632-22-2-222-2-2-2222-22-2−2i−2i2i2i0000-22i2i−2i−2i200000000-2-22200002i−2i00−2i2i2-200000000000000000000000000
χ642-22-2-222-2-2-2222-22-2−2i−2i2i2i0000-2−2i−2i2i2i20000000022-2-200002i−2i002i−2i-2200000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ66444-4-4-4-44-404004-40000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ67444-4-4-4-44-404004-4000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ6844-44-44-4-40404-400-400004-44-400000000000000000000000000000000000000000000000000000000
χ6944-44-44-4-40404-400-40000-44-4400000000000000000000000000000000000000000000000000000000
χ7044-44-44-4-40-40-44004000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ7144-44-44-4-40-40-4400400000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ724-4444-4-4-440400-4-400000000000000022−22−2222−222222−22000000000000000000000000000000000000000000
χ734-4444-4-4-440400-4-4000000000000000−222222−2222−22−2222000000000000000000000000000000000000000000
χ744-44-4-444-44-4-4444-4-40000000040000-400000000000000000000000000000000000000000000000000
χ754-4-4-444-44040-4400-400004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ764-4-4-444-44040-4400-40000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ774-4-4-444-440-404-40040000000000000000000000000000000000000022−22−22220000000000000000000000
χ784-4-4-444-440-404-400400000000000000000000000000000000000000−222222−220000000000000000000000
χ7988-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000

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