Finite Group Databasebeta

← Group #348991

Character table — Group #348991

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11-1-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-11-1-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-111111-1-1-1-111111-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-111111-1-1-1-111111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-2-22-222-2-2220000-20000-20022-2-2-2000000-2-2000022000000000000000000
χ1822222222222-2-2-22-222-2-2220000-20000-200-2-2-222000000220000-2-2000000000000000000
χ1922222222222-2-2-22-2-2-222-2-20000-20000-200222-2-2000000220000-2-2000000000000000000
χ2022222222222-2-2-22-2-2-222-2-20000-20000-200-2-2222000000-2-2000022000000000000000000
χ2122222222-2-2-2222-2222-2-2-2-22222-2-2-2-2-2-2-2-20020000002200000000000000000000000000
χ2222222222-2-2-2222-2222-2-2-2-2-2-2-2-2-22222-222002000000-2-200000000000000000000000000
χ2322222222-2-2-2222-22-2-222222222-22222-2-2-200-2000000-2-200000000000000000000000000
χ2422222222-2-2-2222-22-2-22222-2-2-2-2-2-2-2-2-2-22200-20000002200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200002000020000-20022-2-2000022-2-200000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200002000020000-200-2-2220000-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000200002000020022-2-20000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002000020000200-2-222000022-2-200000000000000000000
χ2922-22-22-2-20002-2-202002-22-22i2i−2i−2i02i2i−2i−2i0000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ3022-22-22-2-20002-2-202002-22-22i2i−2i−2i02i2i−2i−2i0000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ3122-22-22-2-20002-2-202002-22-2−2i−2i2i2i0−2i−2i2i2i0000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ3222-22-22-2-20002-2-202002-22-2−2i−2i2i2i0−2i−2i2i2i0000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ3322-22-22-2-20002-2-20200-22-222i2i−2i−2i0−2i−2i2i2i0000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ3422-22-22-2-20002-2-20200-22-222i2i−2i−2i0−2i−2i2i2i0000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ3522-22-22-2-20002-2-20200-22-22−2i−2i2i2i02i2i−2i−2i0000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ3622-22-22-2-20002-2-20200-22-22−2i−2i2i2i02i2i−2i−2i0000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ372-2-2-2-222222-222-2-2-20000002i−2i2i−2i-2000022i−2i2i−2i02i−2i000000002-22-200000000000000000000
χ382-2-2-2-222222-222-2-2-20000002i−2i2i−2i-2000022i−2i−2i2i0−2i2i00000000-22-2200000000000000000000
χ392-2-2-2-222222-222-2-2-2000000−2i2i−2i2i-200002−2i2i2i−2i02i−2i00000000-22-2200000000000000000000
χ402-2-2-2-222222-222-2-2-2000000−2i2i−2i2i-200002−2i2i−2i2i0−2i2i000000002-22-200000000000000000000
χ412-2-2-2-222222-2-2-22-22000000000022-22-2-2002i−2i0−2i2i2i−2i2i−2i2-200000000000000000000000000
χ422-2-2-2-222222-2-2-22-22000000000022-22-2-200−2i2i02i−2i−2i2i−2i2i2-200000000000000000000000000
χ432-2-2-2-222222-2-2-22-2200000000002-22-22-2002i−2i0−2i2i−2i2i−2i2i-2200000000000000000000000000
χ442-2-2-2-222222-2-2-22-2200000000002-22-22-200−2i2i02i−2i2i−2i2i−2i-2200000000000000000000000000
χ452-2-2-2-2222-2-2222-22-20000002i−2i2i−2i20000-2−2i2i000002i−2i−2i2i002-200002-2000000000000000000
χ462-2-2-2-2222-2-2222-22-20000002i−2i2i−2i20000-2−2i2i00000−2i2i2i−2i00-220000-22000000000000000000
χ472-2-2-2-2222-2-2222-22-2000000−2i2i−2i2i20000-22i−2i000002i−2i−2i2i00-220000-22000000000000000000
χ482-2-2-2-2222-2-2222-22-2000000−2i2i−2i2i20000-22i−2i00000−2i2i2i−2i002-200002-2000000000000000000
χ492-2-2-2-2222-2-22-2-22220000000000-22-22-2200000000000-222-22-2-22-22000000000000000000
χ502-2-2-2-2222-2-22-2-22220000000000-22-22-2200000000000-22-22-222-22-2000000000000000000
χ512-2-2-2-2222-2-22-2-22220000000000-2-22-222000000000002-22-2-222-2-22000000000000000000
χ522-2-2-2-2222-2-22-2-22220000000000-2-22-222000000000002-2-222-2-222-2000000000000000000
χ5344-44-44-4-4000-4440-4004-4-440000000000000000000000000000000000000000000000000
χ5444-44-44-4-4000-4440-400-444-40000000000000000000000000000000000000000000000000
χ5544-4-44-44-44-44000-40000000000000000000000000000000000000000000000000022−220000
χ5644-4-44-44-44-44000-400000000000000000000000000000000000000000000000000−22220000
χ5744-4-44-44-4-44-4000400000000000000000000000000000000000000000000000000002i2−2i200
χ5844-4-44-44-4-44-400040000000000000000000000000000000000000000000000000000−2i22i200
χ594-444-4-44-44-4-40004000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ604-444-4-44-44-4-4000400000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ614-444-4-44-4-444000-400000000000000000000000000000000000000000022−2222−220000000000
χ624-444-4-44-4-444000-4000000000000000000000000000000000000000000−2222−22220000000000
χ634-44-444-4-40004-440-40000004-4-44000000000000000000000000000000000000000000000
χ644-44-444-4-40004-440-4000000-444-4000000000000000000000000000000000000000000000
χ654-44-444-4-4000-44-404000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ664-44-444-4-4000-44-40400000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ674-4-444-4-44000000004i−4i000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ684-4-444-4-44000000004i−4i00000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ694-4-444-4-4400000000−4i4i000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ704-4-444-4-4400000000−4i4i00000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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