Finite Group Databasebeta

← Group #227342

Character table — Group #227342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222224444444444444444448888888888888888888888888888161616161616161616161616
order12222222444444442222444444888888882244444444448888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-111111111-1-111-1-111-1-1-1-1
χ171-11-11-11-111-1-111-1-111-1-1-1ii−i−i1ii−i−iii−i−i1-1i−i1-1i−i1-1i−ii−i11-1-1i−iii−i−i11-1-11-1i−i1-1i−i1-1i−i
χ181-11-11-11-111-1-111-1-111-1-1-1ii−i−i1ii−i−i−i−iii-11i−i1-1i−i-11i−i−ii11-1-1i−i−i−iii-1-1111-1−ii-11i−i-11−ii
χ191-11-11-11-111-1-111-1-111-1-1-1ii−i−i1−i−iiiii−i−i1-1i−i1-1−ii1-1−iii−i-1-111−iiii−i−i-1-111-11−ii1-1i−i-11−ii
χ201-11-11-11-111-1-111-1-111-1-1-1ii−i−i1−i−iii−i−iii-11i−i1-1−ii-11−ii−ii-1-111−ii−i−iii11-1-1-11i−i-11i−i1-1i−i
χ211-11-11-11-111-1-111-1-111-1-1-1−i−iii1ii−i−iii−i−i-11−ii1-1i−i-11i−ii−i-1-111i−iii−i−i11-1-1-11−ii-11−ii1-1−ii
χ221-11-11-11-111-1-111-1-111-1-1-1−i−iii1ii−i−i−i−iii1-1−ii1-1i−i1-1i−i−ii-1-111i−i−i−iii-1-111-11i−i1-1−ii-11i−i
χ231-11-11-11-111-1-111-1-111-1-1-1−i−iii1−i−iiiii−i−i-11−ii1-1−ii-11−iii−i11-1-1−iiii−i−i-1-1111-1i−i-11−ii-11i−i
χ241-11-11-11-111-1-111-1-111-1-1-1−i−iii1−i−iii−i−iii1-1−ii1-1−ii1-1−ii−ii11-1-1−ii−i−iii11-1-11-1−ii1-1−ii1-1−ii
χ251-11-11-11-111-1-111-1-1-1-111-1ii−i−i1ii−i−iii−i−i1-1i−i-11−ii1-1−iii−i11-1-1i−i−i−iii11-1-1-11−ii-11−ii-11i−i
χ261-11-11-11-111-1-111-1-1-1-111-1ii−i−i1ii−i−i−i−iii-11i−i-11−ii-11−ii−ii11-1-1i−iii−i−i-1-111-11i−i1-1−ii1-1−ii
χ271-11-11-11-111-1-111-1-1-1-111-1ii−i−i1−i−iiiii−i−i1-1i−i-11i−i1-1i−ii−i-1-111−ii−i−iii-1-1111-1i−i-11−ii1-1−ii
χ281-11-11-11-111-1-111-1-1-1-111-1ii−i−i1−i−iii−i−iii-11i−i-11i−i-11i−i−ii-1-111−iiii−i−i11-1-11-1−ii1-1−ii-11i−i
χ291-11-11-11-111-1-111-1-1-1-111-1−i−iii1ii−i−iii−i−i-11−ii-11−ii-11−iii−i-1-111i−i−i−iii11-1-11-1i−i1-1i−i-11−ii
χ301-11-11-11-111-1-111-1-1-1-111-1−i−iii1ii−i−i−i−iii1-1−ii-11−ii1-1−ii−ii-1-111i−iii−i−i-1-1111-1−ii-11i−i1-1i−i
χ311-11-11-11-111-1-111-1-1-1-111-1−i−iii1−i−iiiii−i−i-11−ii-11i−i-11i−ii−i11-1-1−ii−i−iii-1-111-11−ii1-1i−i1-1i−i
χ321-11-11-11-111-1-111-1-1-1-111-1−i−iii1−i−iii−i−iii1-1−ii-11i−i1-1i−i−ii11-1-1−iiii−i−i11-1-1-11i−i-11i−i-11−ii
χ33222222222-22-22-22-20000-22222-200002222-2-2-2-200002200-2-200000000000000000000000000
χ34222222222-22-22-22-20000-22222-20000-2-2-2-222-2-20000-2-2002200000000000000000000000000
χ35222222222-22-22-22-20000-2-2-2-2-2-20000222222220000-2-200-2-200000000000000000000000000
χ36222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-2-2-222000022002200000000000000000000000000
χ3722222222-22-22-22-222222-20000-2222200000000-2-2-2-20022000000-2-200000000000000000000
χ3822222222-22-22-22-222222-20000-2-2-2-2-200000000-2-22200-2-20000002200000000000000000000
χ3922222222-22-22-22-22-2-2-2-2-20000-2222200000000222200-2-2000000-2-200000000000000000000
χ4022222222-22-22-22-22-2-2-2-2-20000-2-2-2-2-20000000022-2-200220000002200000000000000000000
χ412-22-22-22-22-2-222-2-22000022i2i−2i−2i-200002i2i−2i−2i-22−2i2i00002-200−2i2i00000000000000000000000000
χ422-22-22-22-22-2-222-2-22000022i2i−2i−2i-20000−2i−2i2i2i2-2−2i2i0000-22002i−2i00000000000000000000000000
χ432-22-22-22-22-2-222-2-2200002−2i−2i2i2i-200002i2i−2i−2i2-22i−2i0000-2200−2i2i00000000000000000000000000
χ442-22-22-22-22-2-222-2-2200002−2i−2i2i2i-20000−2i−2i2i2i-222i−2i00002-2002i−2i00000000000000000000000000
χ452-22-22-22-2-222-2-222-222-2-220000-22i2i−2i−2i00000000-22−2i2i002i−2i000000−2i2i00000000000000000000
χ462-22-22-22-2-222-2-222-222-2-220000-2−2i−2i2i2i00000000-222i−2i00−2i2i0000002i−2i00000000000000000000
χ472-22-22-22-2-222-2-222-2-2-22220000-22i2i−2i−2i000000002-22i−2i00−2i2i000000−2i2i00000000000000000000
χ482-22-22-22-2-222-2-222-2-2-22220000-2−2i−2i2i2i000000002-2−2i2i002i−2i0000002i−2i00000000000000000000
χ4944444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000000
χ50444-4-4-4-4400000000000000000022−2222−222i2−2i22i2−2i20000000000000000000000002i−2i2i−2i000000000000
χ51444-4-4-4-4400000000000000000022−2222−22−2i22i2−2i22i2000000000000000000000000−2i2i−2i2i000000000000
χ52444-4-4-4-44000000000000000000−2222−22222i2−2i22i2−2i2000000000000000000000000−2i2i−2i2i000000000000
χ53444-4-4-4-44000000000000000000−2222−2222−2i22i2−2i22i20000000000000000000000002i−2i2i−2i000000000000
χ5444-444-4-4-44040-40-400000000000000000000000000000000022−2222−220000000000000000000000
χ5544-444-4-4-44040-40-4000000000000000000000000000000000−2222−22220000000000000000000000
χ5644-444-4-4-4-40-404040000004i−4i4i−4i0000000000000000000000000000000000000000000000000
χ5744-444-4-4-4-40-40404000000−4i4i−4i4i0000000000000000000000000000000000000000000000000
χ5844-4-4-444-404040-40-4000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ5944-4-4-444-404040-40-400000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ6044-4-4-444-40-40-404044-44-4000000000000000000000000000000000000000000000000000000
χ6144-4-4-444-40-40-40404-44-44000000000000000000000000000000000000000000000000000000
χ624-444-44-4-40000000000000000002i2−2i2−2i22i222−22−2222000000000000000000000000−2i2i2i−2i000000000000
χ634-444-44-4-40000000000000000002i2−2i2−2i22i2−222222−220000000000000000000000002i−2i−2i2i000000000000
χ644-444-44-4-4000000000000000000−2i22i22i2−2i222−22−22220000000000000000000000002i−2i−2i2i000000000000
χ654-444-44-4-4000000000000000000−2i22i22i2−2i2−222222−22000000000000000000000000−2i2i2i−2i000000000000
χ664-44-44-44-4-4-444-4-4440000-400004000000000000000000000000000000000000000000000000
χ674-4-44-4-444040-40-4040000000000000000000000000000000000000022−22−22220000000000000000
χ684-4-44-4-444040-40-40400000000000000000000000000000000000000−222222−220000000000000000
χ694-4-44-4-4440-404040-44-4-44000000000000000000000000000000000000000000000000000000
χ704-4-44-4-4440-404040-4-444-4000000000000000000000000000000000000000000000000000000
χ714-4-4-444-4440-40-40400000000000000000000000000000000022−22−22220000000000000000000000
χ724-4-4-444-4440-40-404000000000000000000000000000000000−222222−220000000000000000000000
χ734-4-4-444-44-404040-40000004-4-440000000000000000000000000000000000000000000000000
χ744-4-4-444-44-404040-4000000-444-40000000000000000000000000000000000000000000000000

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