Finite Group Databasebeta

← Group #229305

Character table — Group #229305

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888822444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111
χ511111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1
χ91111111111111111-1-1-1-11111111111111111111111-1-1-1-11111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111111111-1-11111-1-1-1-1
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
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ171-11-111-1-1-11-1-1-111111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-11-1i−ii−ii−ii−i1-111-1-111-1-111-1-1ii−i−i1-11-1i−ii−ii−i
χ181-11-111-1-1-11-1-1-111111-1-1ii−i−iii−i−i1-1−i−i−i−iiiii11-1-11-1−iii−ii−i−ii1-1-1-111-1-11111-1-1−i−iii-11-11i−ii−i−ii
χ191-11-111-1-1-11-1-1-111111-1-1ii−i−i−i−iii1-1iiii−i−i−i−i-1-1111-1i−ii−i−iii−i-1111-1-1-1-111-1-111−i−iii1-1-11i−i−ii−ii
χ201-11-111-1-1-11-1-1-111111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-1-1111-1−iii−i−ii−ii-11-1-11111-1-1-1-111ii−i−i-111-1i−i−iii−i
χ211-11-111-1-1-11-1-1-111111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-1-1111-1i−i−iii−ii−i-11-1-11111-1-1-1-111−i−iii-111-1−iii−i−ii
χ221-11-111-1-1-11-1-1-111111-1-1−i−iiiii−i−i1-1−i−i−i−iiiii-1-1111-1−ii−iii−i−ii-1111-1-1-1-111-1-111ii−i−i1-1-11−iii−ii−i
χ231-11-111-1-1-11-1-1-111111-1-1−i−iii−i−iii1-1iiii−i−i−i−i11-1-11-1i−i−ii−iii−i1-1-1-111-1-11111-1-1ii−i−i-11-11−ii−iii−i
χ241-11-111-1-1-11-1-1-111111-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-11-1−ii−ii−ii−ii1-111-1-111-1-111-1-1−i−iii1-11-1−ii−ii−ii
χ251-11-111-1-1-11-1-1-1111-1-111ii−i−iii−i−i1-1iiii−i−i−i−i11-1-1-11−iii−ii−i−ii1-111-1-111-1-1-1-111ii−i−i-11-11−ii−ii−ii
χ261-11-111-1-1-11-1-1-1111-1-111ii−i−iii−i−i1-1−i−i−i−iiiii11-1-1-11i−ii−ii−ii−i1-1-1-111-1-111-1-111−i−iii1-11-1−ii−iii−i
χ271-11-111-1-1-11-1-1-1111-1-111ii−i−i−i−iii1-1iiii−i−i−i−i-1-111-11−iii−i−ii−ii-1111-1-1-1-11111-1-1−i−iii-111-1−iii−ii−i
χ281-11-111-1-1-11-1-1-1111-1-111ii−i−i−i−iii1-1−i−i−i−iiiii-1-111-11i−ii−i−iii−i-11-1-11111-1-111-1-1ii−i−i1-1-11−iii−i−ii
χ291-11-111-1-1-11-1-1-1111-1-111−i−iiiii−i−i1-1iiii−i−i−i−i-1-111-11−ii−iii−i−ii-11-1-11111-1-111-1-1−i−iii1-1-11i−i−iii−i
χ301-11-111-1-1-11-1-1-1111-1-111−i−iiiii−i−i1-1−i−i−i−iiiii-1-111-11i−i−iii−ii−i-1111-1-1-1-11111-1-1ii−i−i-111-1i−i−ii−ii
χ311-11-111-1-1-11-1-1-1111-1-111−i−iii−i−iii1-1iiii−i−i−i−i11-1-1-11−ii−ii−ii−ii1-1-1-111-1-111-1-111ii−i−i1-11-1i−ii−i−ii
χ321-11-111-1-1-11-1-1-1111-1-111−i−iii−i−iii1-1−i−i−i−iiiii11-1-1-11i−i−ii−iii−i1-111-1-111-1-1-1-111−i−iii-11-11i−ii−ii−i
χ332222222222-2-22-2-22000022222222-2-20000000022220000-2-2-2-200-2-200000000000000000000000000
χ342222222222-2-22-2-2200002222-2-2-2-2-2-200000000-2-2-2-20000-2-222002200000000000000000000000000
χ352222222222-2-22-2-220000-2-2-2-22222-2-200000000-2-2-2-2000022-2-2002200000000000000000000000000
χ362222222222-2-22-2-220000-2-2-2-2-2-2-2-2-2-20000000022220000222200-2-200000000000000000000000000
χ3722222222-2-222-222-2222200000000-2-222-2-222-2-20000-2-2220000-2-20000000000000000000000000000
χ3822222222-2-222-222-2222200000000-2-2-2-222-2-2220000-2-2-2-20000220000000000000000000000000000
χ3922222222-2-222-222-2-2-2-2-200000000-2-222-2-222-2-2000022-2-20000220000000000000000000000000000
χ4022222222-2-222-222-2-2-2-2-200000000-2-2-2-222-2-222000022220000-2-20000000000000000000000000000
χ41222-2-2-22-2-2-200200200002i−2i2i−2i2i−2i2i−2i002−22−22−22−22-22-2000000000000i2−i2i2−i2i2−i2i2−i200002−22−20000000000
χ42222-2-2-22-2-2-200200200002i−2i2i−2i2i−2i2i−2i00−22−22−22−222-22-2000000000000−i2i2−i2i2−i2i2−i2i20000−22−220000000000
χ43222-2-2-22-2-2-200200200002i−2i2i−2i−2i2i−2i2i002−22−22−22−2-22-22000000000000i2−i2i2−i2−i2i2−i2i20000−22−220000000000
χ44222-2-2-22-2-2-200200200002i−2i2i−2i−2i2i−2i2i00−22−22−22−22-22-22000000000000−i2i2−i2i2i2−i2i2−i200002−22−20000000000
χ45222-2-2-22-2-2-20020020000−2i2i−2i2i2i−2i2i−2i002−22−22−22−2-22-22000000000000−i2i2−i2i2i2−i2i2−i20000−22−220000000000
χ46222-2-2-22-2-2-20020020000−2i2i−2i2i2i−2i2i−2i00−22−22−22−22-22-22000000000000i2−i2i2−i2−i2i2−i2i200002−22−20000000000
χ47222-2-2-22-2-2-20020020000−2i2i−2i2i−2i2i−2i2i002−22−22−22−22-22-2000000000000−i2i2−i2i2−i2i2−i2i200002−22−20000000000
χ48222-2-2-22-2-2-20020020000−2i2i−2i2i−2i2i−2i2i00−22−22−22−222-22-2000000000000i2−i2i2−i2i2−i2i2−i20000−22−220000000000
χ492-222-2-2-222-200-200200002-2-222-2-2200i2−i2i2−i2−i2i2−i2i22-2-22000000000000−i2i2i2−i2−i2i2i2−i20000i2−i2−i2i20000000000
χ502-222-2-2-222-200-200200002-2-222-2-2200−i2i2−i2i2i2−i2i2−i22-2-22000000000000i2−i2−i2i2i2−i2−i2i20000−i2i2i2−i20000000000
χ512-222-2-2-222-200-200200002-2-22-222-200i2−i2i2−i2−i2i2−i2i2-222-2000000000000−i2i2i2−i2i2−i2−i2i20000−i2i2i2−i20000000000
χ522-222-2-2-222-200-200200002-2-22-222-200−i2i2−i2i2i2−i2i2−i2-222-2000000000000i2−i2−i2i2−i2i2i2−i20000i2−i2−i2i20000000000
χ532-222-2-2-222-200-20020000-222-22-2-2200i2−i2i2−i2−i2i2−i2i2-222-2000000000000i2−i2−i2i2−i2i2i2−i20000−i2i2i2−i20000000000
χ542-222-2-2-222-200-20020000-222-22-2-2200−i2i2−i2i2i2−i2i2−i2-222-2000000000000−i2i2i2−i2i2−i2−i2i20000i2−i2−i2i20000000000
χ552-222-2-2-222-200-20020000-222-2-222-200i2−i2i2−i2−i2i2−i2i22-2-22000000000000i2−i2−i2i2i2−i2−i2i20000i2−i2−i2i20000000000
χ562-222-2-2-222-200-20020000-222-2-222-200−i2i2−i2i2i2−i2i2−i22-2-22000000000000−i2i2i2−i2−i2i2i2−i20000−i2i2i2−i20000000000
χ572-22-222-2-22-2-2-2222-222-2-200000000-222i2i−2i−2i−2i−2i2i2i0000-222i−2i0000−2i2i0000000000000000000000000000
χ582-22-222-2-22-2-2-2222-222-2-200000000-22−2i−2i2i2i2i2i−2i−2i0000-22−2i2i00002i−2i0000000000000000000000000000
χ592-22-222-2-22-2-2-2222-2-2-22200000000-222i2i−2i−2i−2i−2i2i2i00002-2−2i2i00002i−2i0000000000000000000000000000
χ602-22-222-2-22-2-2-2222-2-2-22200000000-22−2i−2i2i2i2i2i−2i−2i00002-22i−2i0000−2i2i0000000000000000000000000000
χ612-22-222-2-2-2222-2-2-2200002i2i−2i−2i2i2i−2i−2i-220000000022-2-20000−2i2i−2i2i00-2200000000000000000000000000
χ622-22-222-2-2-2222-2-2-2200002i2i−2i−2i−2i−2i2i2i-2200000000-2-2220000−2i2i2i−2i002-200000000000000000000000000
χ632-22-222-2-2-2222-2-2-220000−2i−2i2i2i2i2i−2i−2i-2200000000-2-22200002i−2i−2i2i002-200000000000000000000000000
χ642-22-222-2-2-2222-2-2-220000−2i−2i2i2i−2i−2i2i2i-220000000022-2-200002i−2i2i−2i00-2200000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ66444-4-4-44-44400-400-40000000000000022−22−222222−22−2222000000000000000000000000000000000000000000
χ67444-4-4-44-44400-400-400000000000000−222222−22−222222−22000000000000000000000000000000000000000000
χ6844-4-44-4-44004-404-4000000000000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ6944-4-44-4-44004-404-400000000000000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ7044-4-44-4-4400-440-4404i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ7144-4-44-4-4400-440-440−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ724-444-4-4-44-4400400-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ734-444-4-4-44-4400400-400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ744-44-444-4-44-4444-4-4-40000000000004-400000000000000000000000000000000000000000000000000
χ754-4-444-44-4004-40-4404i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ764-4-444-44-4004-40-440−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ774-4-444-44-400-4404-4000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ784-4-444-44-400-4404-400000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ7988-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000

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