Finite Group Databasebeta

← Group #227231

Character table — Group #227231

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444442222444444444488888888888844444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1-1
χ91111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1
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
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-11111
χ171-1-111-1-1111-1-111-1-111-1-1-1ii−i−i11-1-11ii−i−iii−i−iii−i−ii−i1-1i−ii−i1-1i−i11-1-1ii−i−iii−i−i11-1-11-1i−ii−i1-11-1
χ181-1-111-1-1111-1-111-1-111-1-1-1ii−i−i11-1-11−i−iiiii−i−i−i−iii−ii1-1i−i−ii1-1i−i-1-111ii−i−i−i−iii-1-111-11i−i−ii1-1-11
χ191-1-111-1-1111-1-111-1-111-1-1-1ii−i−i-1-1111ii−i−i−i−iiiii−i−ii−i-11i−ii−i1-1−ii11-1-1−i−iii−i−iii-1-1111-1i−i−ii-11-11
χ201-1-111-1-1111-1-111-1-111-1-1-1ii−i−i-1-1111−i−iii−i−iii−i−iii−ii-11i−i−ii1-1−ii-1-111−i−iiiii−i−i11-1-1-11i−ii−i-111-1
χ211-1-111-1-1111-1-111-1-111-1-1-1−i−iii11-1-11ii−i−i−i−iiiii−i−ii−i1-1−iii−i1-1−ii-1-111−i−iiiii−i−i-1-111-11−iii−i1-1-11
χ221-1-111-1-1111-1-111-1-111-1-1-1−i−iii11-1-11−i−iii−i−iii−i−iii−ii1-1−ii−ii1-1−ii11-1-1−i−iii−i−iii11-1-11-1−ii−ii1-11-1
χ231-1-111-1-1111-1-111-1-111-1-1-1−i−iii-1-1111ii−i−iii−i−iii−i−ii−i-11−iii−i1-1i−i-1-111ii−i−i−i−iii11-1-1-11−ii−ii-111-1
χ241-1-111-1-1111-1-111-1-111-1-1-1−i−iii-1-1111−i−iiiii−i−i−i−iii−ii-11−ii−ii1-1i−i11-1-1ii−i−iii−i−i-1-1111-1−iii−i-11-11
χ251-1-111-1-1111-1-111-1-1-1-111-1ii−i−i11-1-11ii−i−iii−i−iii−i−i−ii1-1i−i−ii-11i−i11-1-1−i−iiiii−i−i11-1-1-11−ii−ii-11-11
χ261-1-111-1-1111-1-111-1-1-1-111-1ii−i−i11-1-11−i−iiiii−i−i−i−iiii−i1-1i−ii−i-11i−i-1-111−i−iii−i−iii-1-1111-1−iii−i-111-1
χ271-1-111-1-1111-1-111-1-1-1-111-1ii−i−i-1-1111ii−i−i−i−iiiii−i−i−ii-11i−i−ii-11−ii11-1-1ii−i−i−i−iii-1-111-11−iii−i1-11-1
χ281-1-111-1-1111-1-111-1-1-1-111-1ii−i−i-1-1111−i−iii−i−iii−i−iiii−i-11i−ii−i-11−ii-1-111ii−i−iii−i−i11-1-11-1−ii−ii1-1-11
χ291-1-111-1-1111-1-111-1-1-1-111-1−i−iii11-1-11ii−i−i−i−iiiii−i−i−ii1-1−ii−ii-11−ii-1-111ii−i−iii−i−i-1-1111-1i−i−ii-111-1
χ301-1-111-1-1111-1-111-1-1-1-111-1−i−iii11-1-11−i−iii−i−iii−i−iiii−i1-1−iii−i-11−ii11-1-1ii−i−i−i−iii11-1-1-11i−ii−i-11-11
χ311-1-111-1-1111-1-111-1-1-1-111-1−i−iii-1-1111ii−i−iii−i−iii−i−i−ii-11−ii−ii-11i−i-1-111−i−iii−i−iii11-1-11-1i−ii−i1-1-11
χ321-1-111-1-1111-1-111-1-1-1-111-1−i−iii-1-1111−i−iiiii−i−i−i−iiii−i-11−iii−i-11i−i11-1-1−i−iiiii−i−i-1-111-11i−i−ii1-11-1
χ33222222222-22-22-22-22222-200000000-222220000-2-2-2-2220000-2-2-2-20000000000000000000000000000
χ34222222222-22-22-22-22222-200000000-2-2-2-2-200002222-2-2000022-2-20000000000000000000000000000
χ35222222222-22-22-22-2-2-2-2-2-200000000-222220000-2-2-2-2-2-2000022220000000000000000000000000000
χ36222222222-22-22-22-2-2-2-2-2-200000000-2-2-2-2-200002222220000-2-2220000000000000000000000000000
χ3722222222-22-22-22-220000-222222222-200002222000000-2-2-2-20000-2-200000000000000000000000000
χ3822222222-22-22-22-220000-22222-2-2-2-2-20000-2-2-2-200000022-2-200002200000000000000000000000000
χ3922222222-22-22-22-220000-2-2-2-2-22222-20000-2-2-2-2000000-2-22200002200000000000000000000000000
χ4022222222-22-22-22-220000-2-2-2-2-2-2-2-2-2-20000222200000022220000-2-200000000000000000000000000
χ4122-2-2-22-22020-20-202000002-22-22-22-20i2−i2i2−i22-22-2i2−i2i2−i2000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000000000
χ4222-2-2-22-22020-20-202000002-22-22-22-20−i2i2−i2i22-22-2−i2i2−i2i2000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000000000
χ4322-2-2-22-22020-20-202000002-22-2-22-220i2−i2i2−i2-22-22i2−i2i2−i2000000000000i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i20000000000
χ4422-2-2-22-22020-20-202000002-22-2-22-220−i2i2−i2i2-22-22−i2i2−i2i2000000000000−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i20000000000
χ4522-2-2-22-22020-20-20200000-22-222-22-20i2−i2i2−i2-22-22i2−i2i2−i2000000000000−i2i2−i2i20000i2−i2i2−i2−i2i2−i2i20000000000
χ4622-2-2-22-22020-20-20200000-22-222-22-20−i2i2−i2i2-22-22−i2i2−i2i2000000000000i2−i2i2−i20000−i2i2−i2i2i2−i2i2−i20000000000
χ4722-2-2-22-22020-20-20200000-22-22-22-220i2−i2i2−i22-22-2i2−i2i2−i2000000000000−i2i2−i2i20000−i2i2−i2i2i2−i2i2−i20000000000
χ4822-2-2-22-22020-20-20200000-22-22-22-220−i2i2−i2i22-22-2−i2i2−i2i2000000000000i2−i2i2−i20000i2−i2i2−i2−i2i2−i2i20000000000
χ492-22-2-2-22202020-20-2000002i−2i−2i2i2-2-2202−2−222i−2i−2i2i2−2−22000000000000−i2i2i2−i200002−2−22−i2i2i2−i20000000000
χ502-22-2-2-22202020-20-2000002i−2i−2i2i2-2-220−222−22i−2i−2i2i−222−2000000000000i2−i2−i2i20000−222−2i2−i2−i2i20000000000
χ512-22-2-2-22202020-20-2000002i−2i−2i2i-222-202−2−22−2i2i2i−2i2−2−22000000000000−i2i2i2−i20000−222−2i2−i2−i2i20000000000
χ522-22-2-2-22202020-20-2000002i−2i−2i2i-222-20−222−2−2i2i2i−2i−222−2000000000000i2−i2−i2i200002−2−22−i2i2i2−i20000000000
χ532-22-2-2-22202020-20-200000−2i2i2i−2i2-2-2202−2−22−2i2i2i−2i2−2−22000000000000i2−i2−i2i200002−2−22i2−i2−i2i20000000000
χ542-22-2-2-22202020-20-200000−2i2i2i−2i2-2-220−222−2−2i2i2i−2i−222−2000000000000−i2i2i2−i20000−222−2−i2i2i2−i20000000000
χ552-22-2-2-22202020-20-200000−2i2i2i−2i-222-202−2−222i−2i−2i2i2−2−22000000000000i2−i2−i2i20000−222−2−i2i2i2−i20000000000
χ562-22-2-2-22202020-20-200000−2i2i2i−2i-222-20−222−22i−2i−2i2i−222−2000000000000−i2i2i2−i200002−2−22i2−i2−i2i20000000000
χ572-2-222-2-222-2-222-2-2222-2-2200000000-22i2i−2i−2i0000−2i−2i2i2i2i−2i0000−2i2i-220000000000000000000000000000
χ582-2-222-2-222-2-222-2-2222-2-2200000000-2−2i−2i2i2i00002i2i−2i−2i−2i2i00002i−2i-220000000000000000000000000000
χ592-2-222-2-222-2-222-2-22-2-222200000000-22i2i−2i−2i0000−2i−2i2i2i−2i2i00002i−2i2-20000000000000000000000000000
χ602-2-222-2-222-2-222-2-22-2-222200000000-2−2i−2i2i2i00002i2i−2i−2i2i−2i0000−2i2i2-20000000000000000000000000000
χ612-2-222-2-22-222-2-222-2000022i2i−2i−2i22-2-2-200002i2i−2i−2i000000-22−2i2i0000−2i2i00000000000000000000000000
χ622-2-222-2-22-222-2-222-2000022i2i−2i−2i-2-222-20000−2i−2i2i2i0000002-2−2i2i00002i−2i00000000000000000000000000
χ632-2-222-2-22-222-2-222-200002−2i−2i2i2i22-2-2-20000−2i−2i2i2i000000-222i−2i00002i−2i00000000000000000000000000
χ642-2-222-2-22-222-2-222-200002−2i−2i2i2i-2-222-200002i2i−2i−2i0000002-22i−2i0000−2i2i00000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000400000000400000000000000000000000000000000000000000000000000
χ66444-44-4-4-440-40-404000000000000000000000000000000000000000000022−2222−22000000000000000000
χ67444-44-4-4-440-40-4040000000000000000000000000000000000000000000−2222−2222000000000000000000
χ68444-44-4-4-4-404040-404-44-4000000000000000000000000000000000000000000000000000000000000
χ69444-44-4-4-4-404040-40-44-44000000000000000000000000000000000000000000000000000000000000
χ7044-4-4-44-440-404040-4000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ7144-4-4-44-440-404040-400000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ724-44-4-4-4440-40-404040000000000000022−22−22220000−222222−2200000000000000000000000000000000000000
χ734-44-4-4-4440-40-4040400000000000000−222222−22000022−22−222200000000000000000000000000000000000000
χ744-4-444-4-44-4-444-4-4440000-400000000400000000000000000000000000000000000000000000000000
χ754-4-4-4444-44040-40-400000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ764-4-4-4444-44040-40-40000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ774-4-4-4444-4-40-4040404-4-44000000000000000000000000000000000000000000000000000000000000
χ784-4-4-4444-4-40-404040-444-4000000000000000000000000000000000000000000000000000000000000
χ7988-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000

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