Finite Group Databasebeta

← Group #222517

Character table — Group #222517

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888822444444448888888888888888882222444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1
χ31111111111111111111111111-1-1-1-1111111111111111-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111-1-1-1-111111-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111111111-1-111-1-1-1-1
χ91111111111111111-1-1-1-11111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111111111-1-111-1-111-1-1
χ131111111111111111-1-1-1-11-1-1-1-111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1
χ151111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ171-11-1-11-1111-1-11-11-1ii−i−i111-1-111-1-1-1ii−i−i11-1-111-1-11-11-11-1i−i1-1ii−i−i11-1-1i−iii−i−iii−i−i1-11-1i−ii−ii−i
χ181-11-1-11-1111-1-11-11-1ii−i−i111-1-111-1-1-1ii−i−i-1-111-1-1111-11-1-11i−i-11−i−iii-1-111i−iii−i−i−i−iii1-1-11−iii−i−ii
χ191-11-1-11-1111-1-11-11-1ii−i−i111-1-1-1-111-1ii−i−i11-1-111-1-11-1-11-11i−i-11ii−i−i11-1-1i−i−i−iiiii−i−i-11-11−ii−ii−ii
χ201-11-1-11-1111-1-11-11-1ii−i−i111-1-1-1-111-1ii−i−i-1-111-1-1111-1-111-1i−i1-1−i−iii-1-111i−i−i−iii−i−iii-111-1i−i−iii−i
χ211-11-1-11-1111-1-11-11-1ii−i−i1-1-11111-1-1-1−i−iii11-1-111-1-1-111-11-1i−i1-1ii−i−i-1-111−ii−i−iii−i−iii-11-11i−ii−i−ii
χ221-11-1-11-1111-1-11-11-1ii−i−i1-1-11111-1-1-1−i−iii-1-111-1-111-111-1-11i−i-11−i−iii11-1-1−ii−i−iiiii−i−i-111-1−iii−ii−i
χ231-11-1-11-1111-1-11-11-1ii−i−i1-1-111-1-111-1−i−iii11-1-111-1-1-11-11-11i−i-11ii−i−i-1-111−iiii−i−i−i−iii1-11-1−ii−iii−i
χ241-11-1-11-1111-1-11-11-1ii−i−i1-1-111-1-111-1−i−iii-1-111-1-111-11-111-1i−i1-1−i−iii11-1-1−iiii−i−iii−i−i1-1-11i−i−ii−ii
χ251-11-1-11-1111-1-11-11-1−i−iii111-1-111-1-1-1−i−iii11-1-111-1-11-11-11-1−ii1-1−i−iii11-1-1−ii−i−iii−i−iii1-11-1−ii−ii−ii
χ261-11-1-11-1111-1-11-11-1−i−iii111-1-111-1-1-1−i−iii-1-111-1-1111-11-1-11−ii-11ii−i−i-1-111−ii−i−iiiii−i−i1-1-11i−i−iii−i
χ271-11-1-11-1111-1-11-11-1−i−iii111-1-1-1-111-1−i−iii11-1-111-1-11-1-11-11−ii-11−i−iii11-1-1−iiii−i−i−i−iii-11-11i−ii−ii−i
χ281-11-1-11-1111-1-11-11-1−i−iii111-1-1-1-111-1−i−iii-1-111-1-1111-1-111-1−ii1-1ii−i−i-1-111−iiii−i−iii−i−i-111-1−iii−i−ii
χ291-11-1-11-1111-1-11-11-1−i−iii1-1-11111-1-1-1ii−i−i11-1-111-1-1-111-11-1−ii1-1−i−iii-1-111i−iii−i−iii−i−i-11-11−ii−iii−i
χ301-11-1-11-1111-1-11-11-1−i−iii1-1-11111-1-1-1ii−i−i-1-111-1-111-111-1-11−ii-11ii−i−i11-1-1i−iii−i−i−i−iii-111-1i−i−ii−ii
χ311-11-1-11-1111-1-11-11-1−i−iii1-1-111-1-111-1ii−i−i11-1-111-1-1-11-11-11−ii-11−i−iii-1-111i−i−i−iiiii−i−i1-11-1i−ii−i−ii
χ321-11-1-11-1111-1-11-11-1−i−iii1-1-111-1-111-1ii−i−i-1-111-1-111-11-111-1−ii1-1ii−i−i11-1-1i−i−i−iii−i−iii1-1-11−iii−ii−i
χ332222222222-22-2-2-222222-222220000-2222200000000-2-20000-2-20000000000-2-2000000000000000000
χ342222222222-22-2-2-222222-2-2-2-2-20000-2-2-2-2-200000000220000-2-2000000000022000000000000000000
χ352222222222-22-2-2-22-2-2-2-2-222220000-2-2-2-2-200000000-2-2000022000000000022000000000000000000
χ362222222222-22-2-2-22-2-2-2-2-2-2-2-2-20000-2222200000000220000220000000000-2-2000000000000000000
χ3722222222-2-22-2222-20000-200002222-200002222-2-2-2-200-2-22200-2-20000000000000000000000000000
χ3822222222-2-22-2222-20000-200002222-20000-2-2-2-2222200-2-2-2-200220000000000000000000000000000
χ3922222222-2-22-2222-20000-20000-2-2-2-2-200002222-2-2-2-20022-2-200220000000000000000000000000000
χ4022222222-2-22-2222-20000-20000-2-2-2-2-20000-2-2-2-2222200222200-2-20000000000000000000000000000
χ412222-2-2-2-22-20-200022-22-202i−2i2i−2i000002i−2i2i−2i2−22−22−22−200000000002−22−2i2−i2i2−i2000000i2−i2i2−i20000000000
χ422222-2-2-2-22-20-200022-22-202i−2i2i−2i000002i−2i2i−2i−22−22−22−220000000000−22−22−i2i2−i2i2000000−i2i2−i2i20000000000
χ432222-2-2-2-22-20-200022-22-20−2i2i−2i2i00000−2i2i−2i2i2−22−22−22−200000000002−22−2−i2i2−i2i2000000−i2i2−i2i20000000000
χ442222-2-2-2-22-20-200022-22-20−2i2i−2i2i00000−2i2i−2i2i−22−22−22−220000000000−22−22i2−i2i2−i2000000i2−i2i2−i20000000000
χ452222-2-2-2-22-20-20002-22-2202i−2i2i−2i00000−2i2i−2i2i2−22−22−22−20000000000−22−22i2−i2i2−i2000000−i2i2−i2i20000000000
χ462222-2-2-2-22-20-20002-22-2202i−2i2i−2i00000−2i2i−2i2i−22−22−22−2200000000002−22−2−i2i2−i2i2000000i2−i2i2−i20000000000
χ472222-2-2-2-22-20-20002-22-220−2i2i−2i2i000002i−2i2i−2i2−22−22−22−20000000000−22−22−i2i2−i2i2000000i2−i2i2−i20000000000
χ482222-2-2-2-22-20-20002-22-220−2i2i−2i2i000002i−2i2i−2i−22−22−22−2200000000002−22−2i2−i2i2−i2000000−i2i2−i2i20000000000
χ492-22-22-22-22-202000-22i−2i−2i2i02i−2i−2i2i00000-222-22−2−222−2−220000000000i2−i2−i2i2i2−i2−i2i2000000−222−20000000000
χ502-22-22-22-22-202000-22i−2i−2i2i02i−2i−2i2i00000-222-2−222−2−222−20000000000−i2i2i2−i2−i2i2i2−i20000002−2−220000000000
χ512-22-22-22-22-202000-22i−2i−2i2i0−2i2i2i−2i000002-2-222−2−222−2−220000000000i2−i2−i2i2−i2i2i2−i20000002−2−220000000000
χ522-22-22-22-22-202000-22i−2i−2i2i0−2i2i2i−2i000002-2-22−222−2−222−20000000000−i2i2i2−i2i2−i2−i2i2000000−222−20000000000
χ532-22-22-22-22-202000-2−2i2i2i−2i02i−2i−2i2i000002-2-222−2−222−2−220000000000−i2i2i2−i2i2−i2−i2i20000002−2−220000000000
χ542-22-22-22-22-202000-2−2i2i2i−2i02i−2i−2i2i000002-2-22−222−2−222−20000000000i2−i2−i2i2−i2i2i2−i2000000−222−20000000000
χ552-22-22-22-22-202000-2−2i2i2i−2i0−2i2i2i−2i00000-222-22−2−222−2−220000000000−i2i2i2−i2−i2i2i2−i2000000−222−20000000000
χ562-22-22-22-22-202000-2−2i2i2i−2i0−2i2i2i−2i00000-222-2−222−2−222−20000000000i2−i2−i2i2i2−i2−i2i20000002−2−220000000000
χ572-22-2-22-22222-2-22-2-22i2i−2i−2i-222-2-2000022i2i−2i−2i00000000-220000−2i2i0000000000−2i2i000000000000000000
χ582-22-2-22-22222-2-22-2-22i2i−2i−2i-2-2-22200002−2i−2i2i2i000000002-20000−2i2i00000000002i−2i000000000000000000
χ592-22-2-22-22222-2-22-2-2−2i−2i2i2i-222-2-200002−2i−2i2i2i00000000-2200002i−2i00000000002i−2i000000000000000000
χ602-22-2-22-22222-2-22-2-2−2i−2i2i2i-2-2-222000022i2i−2i−2i000000002-200002i−2i0000000000−2i2i000000000000000000
χ612-22-2-22-22-2-2-222-2220000-2000022-2-22000022-2-2-2-22200-222-200-220000000000000000000000000000
χ622-22-2-22-22-2-2-222-2220000-2000022-2-220000-2-22222-2-200-22-22002-20000000000000000000000000000
χ632-22-2-22-22-2-2-222-2220000-20000-2-2222000022-2-2-2-222002-2-22002-20000000000000000000000000000
χ642-22-2-22-22-2-2-222-2220000-20000-2-22220000-2-22222-2-2002-22-200-220000000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000400000000400000000000000000000000000000000000000000000000000
χ664444-4-4-4-4-4404000-400000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ674444-4-4-4-4-4404000-4000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ6844-4-44-4-4400404-4-4000000000000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ6944-4-44-4-4400404-4-400000000000000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ7044-4-44-4-4400-40-44400000000004-44-4000000000000000000000000000000000000000000000000000
χ7144-4-44-4-4400-40-4440000000000-44-44000000000000000000000000000000000000000000000000000
χ724-44-44-44-4-440-4000400000000000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ734-44-44-44-4-440-40004000000000000000000−222222−2222−22−222200000000000000000000000000000000000000
χ744-44-4-44-44-4-444-44-440000400000000-400000000000000000000000000000000000000000000000000
χ754-4-44-4-4440040-4-4400000000004-4-44000000000000000000000000000000000000000000000000000
χ764-4-44-4-4440040-4-440000000000-444-4000000000000000000000000000000000000000000000000000
χ774-4-44-4-44400-4044-40000000000000000000000000000000000000000000000022−22−222200000000000000
χ784-4-44-4-44400-4044-400000000000000000000000000000000000000000000000−222222−2200000000000000
χ7988-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000000

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