Finite Group Databasebeta

← Group #352521

Character table — Group #352521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444448888888888888888444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ91111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-111-1-1-1-111
χ121111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-11111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111-1-11
χ141111111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-111-1
χ151111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-11-1-11
χ172222222222-2-22-2-2222-2-2-2-2000000000000000022-2-22-222-2-200000000000000000000
χ182222222222-2-22-2-2222-2-2-2-20000000000000000-2-2222-2-2-22200000000000000000000
χ192222222222-2-22-2-22-2-2-2-222000000000000000022-2-2-22-2-22200000000000000000000
χ202222222222-2-22-2-22-2-2-2-2220000000000000000-2-222-2222-2-200000000000000000000
χ2122222222-2-222-222-222-2-22222222222000000000000-2-20000-2-2-2-20000000000000000
χ2222222222-2-222-222-222-2-222-2-2-2-2-2-2-2-2000000000000-2-2000022220000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-22222-2-2-2-2000000000000220000-2-2220000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2-2-2-2-2222200000000000022000022-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000002i2i2i2i−2i−2i−2i−2i0000-22000000002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000−2i−2i−2i−2i2i2i2i2i0000-2200000000−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000002i2i2i2i−2i−2i−2i−2i00002-200000000−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000−2i−2i−2i−2i2i2i2i2i00002-2000000002i2i−2i−2i000000000000
χ2922-222-2-2-2222-2-22-2-2002-200000022-2-2000000002-22-2000000002-22-22-2000000000000
χ3022-222-2-2-2222-2-22-2-2002-200000022-2-200000000-22-22000000002-2-22-22000000000000
χ3122-222-2-2-2222-2-22-2-2002-2000000-2-222000000002-22-200000000-22-22-22000000000000
χ3222-222-2-2-2222-2-22-2-2002-2000000-2-22200000000-22-2200000000-222-22-2000000000000
χ3322-222-2-2-222-22-2-22-200-220022-2-2000022-2-222-2-22-2-220000002-2000000000000000000
χ3422-222-2-2-222-22-2-22-200-220022-2-20000-2-222-2-222-222-20000002-2000000000000000000
χ3522-222-2-2-222-22-2-22-200-2200-2-222000022-2-222-2-2-222-2000000-22000000000000000000
χ3622-222-2-2-222-22-2-22-200-2200-2-2220000-2-222-2-2222-2-22000000-22000000000000000000
χ3722-222-2-2-2-2-22-222-2200-2200000022-2-22i2i−2i−2i−2i−2i2i2i0000002i−2i2i−2i00-220000000000000000
χ3822-222-2-2-2-2-22-222-2200-2200000022-2-2−2i−2i2i2i2i2i−2i−2i000000−2i2i−2i2i00-220000000000000000
χ3922-222-2-2-2-2-22-222-2200-22000000-2-2222i2i−2i−2i−2i−2i2i2i000000−2i2i−2i2i002-20000000000000000
χ4022-222-2-2-2-2-22-222-2200-22000000-2-222−2i−2i2i2i2i2i−2i−2i0000002i−2i2i−2i002-20000000000000000
χ4122-222-2-2-2-2-2-222-222002-20022-2-20000000000000000002i−2i−2i2i-2200−2i2i2i−2i000000000000
χ4222-222-2-2-2-2-2-222-222002-20022-2-2000000000000000000−2i2i2i−2i-22002i−2i−2i2i000000000000
χ4322-222-2-2-2-2-2-222-222002-200-2-2220000000000000000002i−2i−2i2i2-2002i−2i−2i2i000000000000
χ4422-222-2-2-2-2-2-222-222002-200-2-222000000000000000000−2i2i2i−2i2-200−2i2i2i−2i000000000000
χ4522-2-2-222-200-2202-202i−2i002i−2i2-22-22i−2i2i−2i00000000000000000000000000i2−i22−2i2−i22−20000
χ4622-2-2-222-200-2202-202i−2i002i−2i2-22-22i−2i2i−2i00000000000000000000000000−i2i2−22−i2i2−220000
χ4722-2-2-222-200-2202-202i−2i002i−2i-22-22−2i2i−2i2i00000000000000000000000000i2−i22−2−i2i2−220000
χ4822-2-2-222-200-2202-202i−2i002i−2i-22-22−2i2i−2i2i00000000000000000000000000−i2i2−22i2−i22−20000
χ4922-2-2-222-200-2202-20−2i2i00−2i2i2-22-2−2i2i−2i2i00000000000000000000000000i2−i2−22i2−i2−220000
χ5022-2-2-222-200-2202-20−2i2i00−2i2i2-22-2−2i2i−2i2i00000000000000000000000000−i2i22−2−i2i22−20000
χ5122-2-2-222-200-2202-20−2i2i00−2i2i-22-222i−2i2i−2i00000000000000000000000000i2−i2−22−i2i22−20000
χ5222-2-2-222-200-2202-20−2i2i00−2i2i-22-222i−2i2i−2i00000000000000000000000000−i2i22−2i2−i2−220000
χ53444-4-4-4-4400440-4-400000004-4-44000000000000000000000000000000000000000000
χ54444-4-4-4-4400440-4-40000000-444-4000000000000000000000000000000000000000000
χ55444-4-4-4-4400-4-4044000000000004i−4i−4i4i00000000000000000000000000000000000000
χ56444-4-4-4-4400-4-404400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ5744-4-4-444-4004-40-4404i−4i00−4i4i0000000000000000000000000000000000000000000000
χ5844-4-4-444-4004-40-440−4i4i004i−4i0000000000000000000000000000000000000000000000
χ594-444-44-4-44-400400-40000000000000022−2222−2222−2222−22000000000000000000000000000000
χ604-444-44-4-44-400400-400000000000000−2222−2222−2222−2222000000000000000000000000000000
χ614-444-44-4-4-4400-4004000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ624-444-44-4-4-4400-400400000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ634-4-44-4-4444-400-40040000000000000022−22−222222−22−2222000000000000000000000000000000
χ644-4-44-4-4444-400-400400000000000000−222222−22−222222−22000000000000000000000000000000
χ654-4-44-4-444-4400400-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ664-4-44-4-444-4400400-400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ678-88-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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