Finite Group Databasebeta

← Group #229353

Character table — Group #229353

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888822444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111
χ111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-11111-1-111-1-111-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
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
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ1711-11-11-1-11-1-1-11-111ii−i−i1ii−i−iii−i−i-1iiii−i−i−i−i11-1-11-11-1i−ii−ii−i1-1ii−i−i11-1-111-1-1ii−i−i1-11-1i−ii−i1-1
χ1811-11-11-1-11-1-1-11-111ii−i−i1ii−i−iii−i−i-1−i−i−i−iiiii11-1-1-11-11i−ii−ii−i1-1ii−i−i-1-111-1-111−i−iii1-11-1−ii−ii-11
χ1911-11-11-1-11-1-1-11-111ii−i−i1ii−i−i−i−iii-1iiii−i−i−i−i11-1-1-11-11i−i−iii−i1-1−i−iii11-1-111-1-1ii−i−i-11-11−ii−ii-11
χ2011-11-11-1-11-1-1-11-111ii−i−i1ii−i−i−i−iii-1−i−i−i−iiiii11-1-11-11-1i−i−iii−i1-1−i−iii-1-111-1-111−i−iii-11-11i−ii−i1-1
χ2111-11-11-1-11-1-1-11-111ii−i−i1−i−iiiii−i−i-1iiii−i−i−i−i-1-1111-11-1i−ii−i−ii-11−i−iii11-1-1-1-111−i−iii-111-1i−i−ii-11
χ2211-11-11-1-11-1-1-11-111ii−i−i1−i−iiiii−i−i-1−i−i−i−iiiii-1-111-11-11i−ii−i−ii-11−i−iii-1-11111-1-1ii−i−i-111-1−iii−i1-1
χ2311-11-11-1-11-1-1-11-111ii−i−i1−i−iii−i−iii-1iiii−i−i−i−i-1-111-11-11i−i−ii−ii-11ii−i−i11-1-1-1-111−i−iii1-1-11−iii−i1-1
χ2411-11-11-1-11-1-1-11-111ii−i−i1−i−iii−i−iii-1−i−i−i−iiiii-1-1111-11-1i−i−ii−ii-11ii−i−i-1-11111-1-1ii−i−i1-1-11i−i−ii-11
χ2511-11-11-1-11-1-1-11-111−i−iii1ii−i−iii−i−i-1iiii−i−i−i−i-1-1111-11-1−iii−ii−i-11−i−iii-1-11111-1-1−i−iii1-1-11−iii−i-11
χ2611-11-11-1-11-1-1-11-111−i−iii1ii−i−iii−i−i-1−i−i−i−iiiii-1-111-11-11−iii−ii−i-11−i−iii11-1-1-1-111ii−i−i1-1-11i−i−ii1-1
χ2711-11-11-1-11-1-1-11-111−i−iii1ii−i−i−i−iii-1iiii−i−i−i−i-1-111-11-11−ii−iii−i-11ii−i−i-1-11111-1-1−i−iii-111-1i−i−ii1-1
χ2811-11-11-1-11-1-1-11-111−i−iii1ii−i−i−i−iii-1−i−i−i−iiiii-1-1111-11-1−ii−iii−i-11ii−i−i11-1-1-1-111ii−i−i-111-1−iii−i-11
χ2911-11-11-1-11-1-1-11-111−i−iii1−i−iiiii−i−i-1iiii−i−i−i−i11-1-11-11-1−iii−i−ii1-1ii−i−i-1-111-1-111ii−i−i-11-11−ii−ii1-1
χ3011-11-11-1-11-1-1-11-111−i−iii1−i−iiiii−i−i-1−i−i−i−iiiii11-1-1-11-11−iii−i−ii1-1ii−i−i11-1-111-1-1−i−iii-11-11i−ii−i-11
χ3111-11-11-1-11-1-1-11-111−i−iii1−i−iii−i−iii-1iiii−i−i−i−i11-1-1-11-11−ii−ii−ii1-1−i−iii-1-111-1-111ii−i−i1-11-1i−ii−i-11
χ3211-11-11-1-11-1-1-11-111−i−iii1−i−iii−i−iii-1−i−i−i−iiiii11-1-11-11-1−ii−ii−ii1-1−i−iii11-1-111-1-1−i−iii1-11-1−ii−ii1-1
χ33222222222-222-2-2-220000-200002222-222-2-222-2-2000022-2-200-2-2000000000000000000000000000000
χ34222222222-222-2-2-220000-200002222-2-2-222-2-2220000-2-22200-2-2000000000000000000000000000000
χ35222222222-222-2-2-220000-20000-2-2-2-2-222-2-222-2-20000-2-2220022000000000000000000000000000000
χ36222222222-222-2-2-220000-20000-2-2-2-2-2-2-222-2-222000022-2-20022000000000000000000000000000000
χ3722222222-22-2-2222-22222-222220000-20000000022220000-2-200-2-2-2-200000000000000000000000000
χ3822222222-22-2-2222-22222-2-2-2-2-20000-200000000-2-2-2-20000-2-200222200000000000000000000000000
χ3922222222-22-2-2222-2-2-2-2-2-222220000-200000000-2-2-2-200002200-2-22200000000000000000000000000
χ4022222222-22-2-2222-2-2-2-2-2-2-2-2-2-20000-20000000022220000220022-2-200000000000000000000000000
χ4122-22-22-2-222-2-2-22-220000-200002i2i−2i−2i22i2i−2i−2i−2i−2i2i2i00002-2-2200−2i2i000000000000000000000000000000
χ4222-22-22-2-222-2-2-22-220000-200002i2i−2i−2i2−2i−2i2i2i2i2i−2i−2i0000-222-200−2i2i000000000000000000000000000000
χ4322-22-22-2-222-2-2-22-220000-20000−2i−2i2i2i22i2i−2i−2i−2i−2i2i2i0000-222-2002i−2i000000000000000000000000000000
χ4422-22-22-2-222-2-2-22-220000-20000−2i−2i2i2i2−2i−2i2i2i2i2i−2i−2i00002-2-22002i−2i000000000000000000000000000000
χ4522-22-22-2-2-2-2222-22-22i2i−2i−2i-22i2i−2i−2i000020000000022-2-20000−2i2i00−2i2i-2200000000000000000000000000
χ4622-22-22-2-2-2-2222-22-22i2i−2i−2i-2−2i−2i2i2i0000200000000-2-2220000−2i2i002i−2i2-200000000000000000000000000
χ4722-22-22-2-2-2-2222-22-2−2i−2i2i2i-22i2i−2i−2i0000200000000-2-22200002i−2i00−2i2i2-200000000000000000000000000
χ4822-22-22-2-2-2-2222-22-2−2i−2i2i2i-2−2i−2i2i2i000020000000022-2-200002i−2i002i−2i-2200000000000000000000000000
χ492-222-2-22-20-20022-202-22-202i−2i2i−2i00000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000000000000000i2−i2i2−i22−22−22−22−20000000000
χ502-222-2-22-20-20022-202-22-202i−2i2i−2i00000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000000000−i2i2−i2i2−22−22−22−220000000000
χ512-222-2-22-20-20022-202-22-20−2i2i−2i2i00000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000000000i2−i2i2−i2−22−22−22−220000000000
χ522-222-2-22-20-20022-202-22-20−2i2i−2i2i00000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000000000000000−i2i2−i2i22−22−22−22−20000000000
χ532-222-2-22-20-20022-20-22-2202i−2i2i−2i00000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000000000−i2i2−i2i22−22−2−22−220000000000
χ542-222-2-22-20-20022-20-22-2202i−2i2i−2i00000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000000000000000i2−i2i2−i2−22−222−22−20000000000
χ552-222-2-22-20-20022-20-22-220−2i2i−2i2i00000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000000000000000−i2i2−i2i2−22−222−22−20000000000
χ562-222-2-22-20-20022-20-22-220−2i2i−2i2i00000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000000000i2−i2i2−i22−22−2−22−220000000000
χ572-2-222-2-2202002-2-202i−2i−2i2i02-2-22000002−22−2−22−22−2i2i2i−2i0000000000000000−i2i2i2−i22−2−22i2−i2−i2i20000000000
χ582-2-222-2-2202002-2-202i−2i−2i2i02-2-2200000−22−222−22−2−2i2i2i−2i0000000000000000i2−i2−i2i2−222−2−i2i2i2−i20000000000
χ592-2-222-2-2202002-2-202i−2i−2i2i0-222-2000002−22−2−22−222i−2i−2i2i0000000000000000−i2i2i2−i2−222−2−i2i2i2−i20000000000
χ602-2-222-2-2202002-2-202i−2i−2i2i0-222-200000−22−222−22−22i−2i−2i2i0000000000000000i2−i2−i2i22−2−22i2−i2−i2i20000000000
χ612-2-222-2-2202002-2-20−2i2i2i−2i02-2-22000002−22−2−22−222i−2i−2i2i0000000000000000i2−i2−i2i22−2−22−i2i2i2−i20000000000
χ622-2-222-2-2202002-2-20−2i2i2i−2i02-2-2200000−22−222−22−22i−2i−2i2i0000000000000000−i2i2i2−i2−222−2i2−i2−i2i20000000000
χ632-2-222-2-2202002-2-20−2i2i2i−2i0-222-2000002−22−2−22−22−2i2i2i−2i0000000000000000i2−i2−i2i2−222−2i2−i2−i2i20000000000
χ642-2-222-2-2202002-2-20−2i2i2i−2i0-222-200000−22−222−22−2−2i2i2i−2i0000000000000000−i2i2i2−i22−2−22−i2i2i2−i20000000000
χ6544444444-4-4-4-4-4-4-4-40000400000000400000000000000000000000000000000000000000000000000
χ66444-44-4-4-4404-4000-40000000000000000000000000000000000000022−2222−220000000000000000000000
χ67444-44-4-4-4404-4000-400000000000000000000000000000000000000−2222−22220000000000000000000000
χ68444-44-4-4-4-40-4400040000000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ69444-44-4-4-4-40-440004000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ7044-44-44-4-4-4444-44-4-40000400000000-400000000000000000000000000000000000000000000000000
χ7144-4-4-4-44440-44000-4000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ7244-4-4-4-44440-44000-400000000000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ7344-4-4-4-444-404-400040000000004-4-44000000000000000000000000000000000000000000000000000
χ7444-4-4-4-444-404-40004000000000-444-4000000000000000000000000000000000000000000000000000
χ754-444-4-44-40400-4-440000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ764-444-4-44-40400-4-44000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ774-4-444-4-440-400-44400000000000000022−22−2222−222222−22000000000000000000000000000000000000000000
χ784-4-444-4-440-400-444000000000000000−222222−2222−22−2222000000000000000000000000000000000000000000
χ798-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000

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