Finite Group Databasebeta

← Group #229362

Character table — Group #229362

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888844444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-11111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-111
χ511111111111111111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111
χ711111111111111111111-1-1-1-11-1-1-1-1111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-111-1-1-1-111-1-1
χ91111111111111111-1-1-1-11111111111111111111111-1-111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ101111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111
χ171-11-1-111-1-1-1-1111-11ii−i−iii−i−i1ii−i−i-111-1-1iiii−i−i−i−i1-1i−i1-1i−ii−iii−i−i11-1-111-1-11-1ii−i−ii−i1-11-1i−i1-1
χ181-11-1-111-1-1-1-1111-11ii−i−iii−i−i1ii−i−i-111-1-1−i−i−i−iiiii-11i−i-11i−ii−iii−i−i-1-111-1-1111-1−i−iii−ii1-11-1−ii-11
χ191-11-1-111-1-1-1-1111-11ii−i−iii−i−i1−i−iii-1-1-111iiii−i−i−i−i1-1−ii1-1i−ii−i−i−iii11-1-1-1-111-11−i−iii−ii-111-1i−i-11
χ201-11-1-111-1-1-1-1111-11ii−i−iii−i−i1−i−iii-1-1-111−i−i−i−iiiii-11−ii-11i−ii−i−i−iii-1-11111-1-1-11ii−i−ii−i-111-1−ii1-1
χ211-11-1-111-1-1-1-1111-11ii−i−i−i−iii1ii−i−i-1-1-111iiii−i−i−i−i1-1i−i1-1i−i−ii−i−iii-1-11111-1-1-11−i−iiii−i1-1-11−ii-11
χ221-11-1-111-1-1-1-1111-11ii−i−i−i−iii1ii−i−i-1-1-111−i−i−i−iiiii-11i−i-11i−i−ii−i−iii11-1-1-1-111-11ii−i−i−ii1-1-11i−i1-1
χ231-11-1-111-1-1-1-1111-11ii−i−i−i−iii1−i−iii-111-1-1iiii−i−i−i−i1-1−ii1-1i−i−iiii−i−i-1-111-1-1111-1ii−i−i−ii-11-11−ii1-1
χ241-11-1-111-1-1-1-1111-11ii−i−i−i−iii1−i−iii-111-1-1−i−i−i−iiiii-11−ii-11i−i−iiii−i−i11-1-111-1-11-1−i−iiii−i-11-11i−i-11
χ251-11-1-111-1-1-1-1111-11−i−iiiii−i−i1ii−i−i-111-1-1iiii−i−i−i−i-11i−i-11−iii−i−i−iii11-1-111-1-11-1ii−i−i−ii-11-11−ii-11
χ261-11-1-111-1-1-1-1111-11−i−iiiii−i−i1ii−i−i-111-1-1−i−i−i−iiiii1-1i−i1-1−iii−i−i−iii-1-111-1-1111-1−i−iiii−i-11-11i−i1-1
χ271-11-1-111-1-1-1-1111-11−i−iiiii−i−i1−i−iii-1-1-111iiii−i−i−i−i-11−ii-11−iii−iii−i−i11-1-1-1-111-11−i−iiii−i1-1-11−ii1-1
χ281-11-1-111-1-1-1-1111-11−i−iiiii−i−i1−i−iii-1-1-111−i−i−i−iiiii1-1−ii1-1−iii−iii−i−i-1-11111-1-1-11ii−i−i−ii1-1-11i−i-11
χ291-11-1-111-1-1-1-1111-11−i−iii−i−iii1ii−i−i-1-1-111iiii−i−i−i−i-11i−i-11−ii−iiii−i−i-1-11111-1-1-11−i−iii−ii-111-1i−i1-1
χ301-11-1-111-1-1-1-1111-11−i−iii−i−iii1ii−i−i-1-1-111−i−i−i−iiiii1-1i−i1-1−ii−iiii−i−i11-1-1-1-111-11ii−i−ii−i-111-1−ii-11
χ311-11-1-111-1-1-1-1111-11−i−iii−i−iii1−i−iii-111-1-1iiii−i−i−i−i-11−ii-11−ii−ii−i−iii-1-111-1-1111-1ii−i−ii−i1-11-1i−i-11
χ321-11-1-111-1-1-1-1111-11−i−iii−i−iii1−i−iii-111-1-1−i−i−i−iiiii1-1−ii1-1−ii−ii−i−iii11-1-111-1-11-1−i−iii−ii1-11-1−ii1-1
χ33222222222-2-22-2-22200002222-22222-222220000000000-2-20000-2-2000000000000-2-200000000000000
χ34222222222-2-22-2-22200002222-2-2-2-2-2-2-2-2-2-20000000000220000-2-20000000000002200000000000000
χ35222222222-2-22-2-2220000-2-2-2-2-22222-2-2-2-2-20000000000-2-20000220000000000002200000000000000
χ36222222222-2-22-2-2220000-2-2-2-2-2-2-2-2-2-22222000000000022000022000000000000-2-200000000000000
χ3722222222-222-222-2-222220000-20000-2000022-2-222-2-22200-2-2-2-2000000000000000000000000000000
χ3822222222-222-222-2-222220000-20000-20000-2-222-2-222-2-20022-2-2000000000000000000000000000000
χ3922222222-222-222-2-2-2-2-2-20000-20000-2000022-2-222-2-2-2-2002222000000000000000000000000000000
χ4022222222-222-222-2-2-2-2-2-20000-20000-20000-2-222-2-2222200-2-222000000000000000000000000000000
χ4122-2-2-22-22200-200-2200002i−2i2i−2i02-22-202i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000002−22−2i2−i2i2−i2002−22−20000000000
χ4222-2-2-22-22200-200-2200002i−2i2i−2i02-22-202i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000000000−22−22−i2i2−i2i200−22−220000000000
χ4322-2-2-22-22200-200-2200002i−2i2i−2i0-22-220−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000002−22−2−i2i2−i2i200−22−220000000000
χ4422-2-2-22-22200-200-2200002i−2i2i−2i0-22-220−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000000000−22−22i2−i2i2−i2002−22−20000000000
χ4522-2-2-22-22200-200-220000−2i2i−2i2i02-22-20−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000000000−22−22i2−i2i2−i200−22−220000000000
χ4622-2-2-22-22200-200-220000−2i2i−2i2i02-22-20−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000002−22−2−i2i2−i2i2002−22−20000000000
χ4722-2-2-22-22200-200-220000−2i2i−2i2i0-22-2202i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000000000−22−22−i2i2−i2i2002−22−20000000000
χ4822-2-2-22-22200-200-220000−2i2i−2i2i0-22-2202i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000002−22−2i2−i2i2−i200−22−220000000000
χ492-22-2-222-22-2-2-2222-22i2i−2i−2i0000-20000200002i2i−2i−2i−2i−2i2i2i2-200-22−2i2i000000000000000000000000000000
χ502-22-2-222-22-2-2-2222-22i2i−2i−2i0000-2000020000−2i−2i2i2i2i2i−2i−2i-22002-2−2i2i000000000000000000000000000000
χ512-22-2-222-22-2-2-2222-2−2i−2i2i2i0000-20000200002i2i−2i−2i−2i−2i2i2i-22002-22i−2i000000000000000000000000000000
χ522-22-2-222-22-2-2-2222-2−2i−2i2i2i0000-2000020000−2i−2i2i2i2i2i−2i−2i2-200-222i−2i000000000000000000000000000000
χ532-22-2-222-2-2222-2-2-2200002i2i−2i−2i-22i2i−2i−2i222-2-20000000000−2i2i0000−2i2i000000000000-2200000000000000
χ542-22-2-222-2-2222-2-2-2200002i2i−2i−2i-2−2i−2i2i2i2-2-22200000000002i−2i0000−2i2i0000000000002-200000000000000
χ552-22-2-222-2-2222-2-2-220000−2i−2i2i2i-22i2i−2i−2i2-2-2220000000000−2i2i00002i−2i0000000000002-200000000000000
χ562-22-2-222-2-2222-2-2-220000−2i−2i2i2i-2−2i−2i2i2i222-2-200000000002i−2i00002i−2i000000000000-2200000000000000
χ572-2-2222-2-2-200-2002200002-2-2202i−2i−2i2i0−2i2i2i−2i2−22−2−22−22000000000000002−2−22−i2i2i2−i200i2−i2−i2i20000000000
χ582-2-2222-2-2-200-2002200002-2-2202i−2i−2i2i0−2i2i2i−2i−22−222−22−200000000000000−222−2i2−i2−i2i200−i2i2i2−i20000000000
χ592-2-2222-2-2-200-2002200002-2-220−2i2i2i−2i02i−2i−2i2i2−22−2−22−22000000000000002−2−22i2−i2−i2i200−i2i2i2−i20000000000
χ602-2-2222-2-2-200-2002200002-2-220−2i2i2i−2i02i−2i−2i2i−22−222−22−200000000000000−222−2−i2i2i2−i200i2−i2−i2i20000000000
χ612-2-2222-2-2-200-200220000-222-202i−2i−2i2i02i−2i−2i2i2−22−2−22−2200000000000000−222−2−i2i2i2−i200−i2i2i2−i20000000000
χ622-2-2222-2-2-200-200220000-222-202i−2i−2i2i02i−2i−2i2i−22−222−22−2000000000000002−2−22i2−i2−i2i200i2−i2−i2i20000000000
χ632-2-2222-2-2-200-200220000-222-20−2i2i2i−2i0−2i2i2i−2i2−22−2−22−2200000000000000−222−2i2−i2−i2i200i2−i2−i2i20000000000
χ642-2-2222-2-2-200-200220000-222-20−2i2i2i−2i0−2i2i2i−2i−22−222−22−2000000000000002−2−22−i2i2i2−i200−i2i2i2−i20000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ664444-4-4-4-404-404-40000000000000000000000000000000000000022−2222−22000000000000000000000000
χ674444-4-4-4-404-404-400000000000000000000000000000000000000−2222−2222000000000000000000000000
χ684444-4-4-4-40-440-44004-44-4000000000000000000000000000000000000000000000000000000000000
χ694444-4-4-4-40-440-4400-44-44000000000000000000000000000000000000000000000000000000000000
χ7044-4-4-44-44-4004004-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ7144-4-4-44-44-4004004-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ724-44-44-4-4404-40-44004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ734-44-44-4-4404-40-4400−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ744-44-44-4-440-4404-4000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ754-44-44-4-440-4404-400000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ764-44-4-444-4444-4-4-44-40000000040000-400000000000000000000000000000000000000000000000000
χ774-4-4444-4-4400400-4-400000000000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ784-4-4444-4-4400400-4-4000000000000000000−222222−2222−22−222200000000000000000000000000000000000000
χ7988-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000

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