Finite Group Databasebeta

← Group #220752

Character table — Group #220752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888822444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1
χ91111111111111111-1-1-1-11111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1
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
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111
χ171-1-11-11-11-1111-1-11-111-1-111-1-111-1-11-111-1-1ii−i−iii−i−i1-1i−ii−i1-11-11-111-1-1ii−i−iii−i−iii−i−i1-1i−ii−i1-1i−i
χ181-1-11-11-11-1111-1-11-111-1-111-1-111-1-11-111-1-1−i−iii−i−iii1-1−ii−ii1-11-11-111-1-1−i−iii−i−iii−i−iii1-1−ii−ii1-1−ii
χ191-1-11-11-11-1111-1-11-111-1-111-1-1-1-1111-111-1-1ii−i−iii−i−i1-1−ii−ii1-1-111-1-1-111ii−i−iii−i−iii−i−i-11−ii−ii-11−ii
χ201-1-11-11-11-1111-1-11-111-1-111-1-1-1-1111-111-1-1−i−iii−i−iii1-1i−ii−i1-1-111-1-1-111−i−iii−i−iii−i−iii-11i−ii−i-11i−i
χ211-1-11-11-11-1111-1-11-111-1-1-1-11111-1-11-1-1-111ii−i−iii−i−i-11i−ii−i1-11-1-11-1-111ii−i−i−i−iii−i−iii-11−iii−i1-1−ii
χ221-1-11-11-11-1111-1-11-111-1-1-1-11111-1-11-1-1-111−i−iii−i−iii-11−ii−ii1-11-1-11-1-111−i−iiiii−i−iii−i−i-11i−i−ii1-1i−i
χ231-1-11-11-11-1111-1-11-111-1-1-1-111-1-1111-1-1-111ii−i−iii−i−i-11−ii−ii1-1-11-1111-1-1ii−i−i−i−iii−i−iii1-1i−i−ii-11i−i
χ241-1-11-11-11-1111-1-11-111-1-1-1-111-1-1111-1-1-111−i−iii−i−iii-11i−ii−i1-1-11-1111-1-1−i−iiiii−i−iii−i−i1-1−iii−i-11−ii
χ251-1-11-11-11-1111-1-11-1-1-11111-1-111-1-11-1-1-111ii−i−iii−i−i1-1i−ii−i-111-1-11-1-111−i−iiiii−i−i−i−iii1-1i−i−ii-11−ii
χ261-1-11-11-11-1111-1-11-1-1-11111-1-111-1-11-1-1-111−i−iii−i−iii1-1−ii−ii-111-1-11-1-111ii−i−i−i−iiiii−i−i1-1−iii−i-11i−i
χ271-1-11-11-11-1111-1-11-1-1-11111-1-1-1-1111-1-1-111ii−i−iii−i−i1-1−ii−ii-11-11-1111-1-1−i−iiiii−i−i−i−iii-11−iii−i1-1i−i
χ281-1-11-11-11-1111-1-11-1-1-11111-1-1-1-1111-1-1-111−i−iii−i−iii1-1i−ii−i-11-11-1111-1-1ii−i−i−i−iiiii−i−i-11i−i−ii1-1−ii
χ291-1-11-11-11-1111-1-11-1-1-111-1-11111-1-11-111-1-1ii−i−iii−i−i-11i−ii−i-111-11-111-1-1−i−iii−i−iiiii−i−i-11−ii−ii-11i−i
χ301-1-11-11-11-1111-1-11-1-1-111-1-11111-1-11-111-1-1−i−iii−i−iii-11−ii−ii-111-11-111-1-1ii−i−iii−i−i−i−iii-11i−ii−i-11−ii
χ311-1-11-11-11-1111-1-11-1-1-111-1-111-1-1111-111-1-1ii−i−iii−i−i-11−ii−ii-11-111-1-1-111−i−iii−i−iiiii−i−i1-1i−ii−i1-1−ii
χ321-1-11-11-11-1111-1-11-1-1-111-1-111-1-1111-111-1-1−i−iii−i−iii-11i−ii−i-11-111-1-1-111ii−i−iii−i−i−i−iii1-1−ii−ii1-1i−i
χ33222222222-2-22-222-2222222220000-2-2222200000000-2-20000-2-200-2-200000000000000000000000000
χ34222222222-2-22-222-22222-2-2-2-20000-2-2-2-2-2-200000000220000-2-2002200000000000000000000000000
χ35222222222-2-22-222-2-2-2-2-222220000-2-2-2-2-2-200000000-2-2000022002200000000000000000000000000
χ36222222222-2-22-222-2-2-2-2-2-2-2-2-20000-2-22222000000002200002200-2-200000000000000000000000000
χ3722222222-222-22-2-22000000002222-2-200002222-2-2-2-20022-2-200-2-20000000000000000000000000000
χ3822222222-222-22-2-22000000002222-2-20000-2-2-2-2222200-2-22200-2-20000000000000000000000000000
χ3922222222-222-22-2-2200000000-2-2-2-2-2-200002222-2-2-2-200-2-22200220000000000000000000000000000
χ4022222222-222-22-2-2200000000-2-2-2-2-2-20000-2-2-2-222220022-2-200220000000000000000000000000000
χ4122-222-2-2-2-200-202202-22-22i−2i2i−2i0000002i−2i2i−2i2−22−22−22−200000000000000002−22−2i2−i2i2−i2i2−i2i2−i20000000000
χ4222-222-2-2-2-200-202202-22-22i−2i2i−2i0000002i−2i2i−2i−22−22−22−220000000000000000−22−22−i2i2−i2i2−i2i2−i2i20000000000
χ4322-222-2-2-2-200-202202-22-2−2i2i−2i2i000000−2i2i−2i2i2−22−22−22−200000000000000002−22−2−i2i2−i2i2−i2i2−i2i20000000000
χ4422-222-2-2-2-200-202202-22-2−2i2i−2i2i000000−2i2i−2i2i−22−22−22−220000000000000000−22−22i2−i2i2−i2i2−i2i2−i20000000000
χ4522-222-2-2-2-200-20220-22-222i−2i2i−2i000000−2i2i−2i2i2−22−22−22−20000000000000000−22−22i2−i2i2−i2−i2i2−i2i20000000000
χ4622-222-2-2-2-200-20220-22-222i−2i2i−2i000000−2i2i−2i2i−22−22−22−2200000000000000002−22−2−i2i2−i2i2i2−i2i2−i20000000000
χ4722-222-2-2-2-200-20220-22-22−2i2i−2i2i0000002i−2i2i−2i2−22−22−22−20000000000000000−22−22−i2i2−i2i2i2−i2i2−i20000000000
χ4822-222-2-2-2-200-20220-22-22−2i2i−2i2i0000002i−2i2i−2i−22−22−22−2200000000000000002−22−2i2−i2i2−i2−i2i2−i2i20000000000
χ492-222-2-22-2200-20-2202-2-222i−2i−2i2i0000002i−2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000i2−i2−i2i2−222−2−222−20000000000
χ502-222-2-22-2200-20-2202-2-222i−2i−2i2i0000002i−2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000−i2i2i2−i22−2−222−2−220000000000
χ512-222-2-22-2200-20-2202-2-22−2i2i2i−2i000000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000i2−i2−i2i22−2−222−2−220000000000
χ522-222-2-22-2200-20-2202-2-22−2i2i2i−2i000000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000−i2i2i2−i2−222−2−222−20000000000
χ532-222-2-22-2200-20-220-222-22i−2i−2i2i000000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000−i2i2i2−i2−222−22−2−220000000000
χ542-222-2-22-2200-20-220-222-22i−2i−2i2i000000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000i2−i2−i2i22−2−22−222−20000000000
χ552-222-2-22-2200-20-220-222-2−2i2i2i−2i0000002i−2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000−i2i2i2−i22−2−22−222−20000000000
χ562-222-2-22-2200-20-220-222-2−2i2i2i−2i0000002i−2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000i2−i2−i2i2−222−22−2−220000000000
χ572-2-22-22-22222-2-22-2-20000000022-2-2-2200002i2i−2i−2i−2i−2i2i2i002i−2i−2i2i00-220000000000000000000000000000
χ582-2-22-22-22222-2-22-2-20000000022-2-2-220000−2i−2i2i2i2i2i−2i−2i00−2i2i2i−2i00-220000000000000000000000000000
χ592-2-22-22-22222-2-22-2-200000000-2-222-2200002i2i−2i−2i−2i−2i2i2i00−2i2i2i−2i002-20000000000000000000000000000
χ602-2-22-22-22222-2-22-2-200000000-2-222-220000−2i−2i2i2i2i2i−2i−2i002i−2i−2i2i002-20000000000000000000000000000
χ612-2-22-22-22-2-2-222-22222-2-222-2-20000-2222-2-200000000-220000-2200-2200000000000000000000000000
χ622-2-22-22-22-2-2-222-22222-2-2-2-2220000-22-2-222000000002-20000-22002-200000000000000000000000000
χ632-2-22-22-22-2-2-222-222-2-22222-2-20000-22-2-22200000000-2200002-2002-200000000000000000000000000
χ642-2-22-22-22-2-2-222-222-2-222-2-2220000-2222-2-2000000002-200002-200-2200000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ66444-4-44-4-404-40400-4000000004-44-40000000000000000000000000000000000000000000000000000
χ67444-4-44-4-404-40400-400000000-44-440000000000000000000000000000000000000000000000000000
χ68444-4-44-4-40-440-4004000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ69444-4-44-4-40-440-400400000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ7044-444-4-4-440040-4-4000000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ7144-444-4-4-440040-4-40000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ724-444-4-44-4-400404-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ734-444-4-44-4-400404-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ744-4-44-44-444-4-4-444-440000000000004-400000000000000000000000000000000000000000000000000
χ754-4-4-4444-404-40-4004000000004-4-440000000000000000000000000000000000000000000000000000
χ764-4-4-4444-404-40-400400000000-444-40000000000000000000000000000000000000000000000000000
χ774-4-4-4444-40-440400-4000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ784-4-4-4444-40-440400-400000000000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ7988-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000

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