Finite Group Databasebeta

← Group #305939

Character table — Group #305939

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442222448888888844444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-11
χ91111111111111111-1-1-1-11111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ101111111111111111-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111111-1-1-111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-111111-1-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111-1-1-1-1-111-11
χ172222222222-2-2-222-22222-2-200000000-2-22200-2-2000000000022-2-20000000000000000
χ182222222222-2-2-222-22222-2-200000000-2-2-2-200220000000000-2-2220000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000222200-2-20000000000-2-2220000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-20000000022-2-20022000000000022-2-20000000000000000
χ2122222222-2-2222-2-220000-2-22222-2-2-2-200002200-2-20000000000000000200-200000000
χ2222222222-2-2222-2-220000-2-22222-2-2-2-20000-2-200220000000000000000-200200000000
χ2322222222-2-2222-2-220000-2-2-2-2-2-2222200002200220000000000000000-200-200000000
χ2422222222-2-2222-2-220000-2-2-2-2-2-222220000-2-200-2-20000000000000000200200000000
χ252222-2-2-2-2222-22-2-2-222-2-2-22000000002-20000000022-2-20000000022-2-2000000000000
χ262222-2-2-2-2222-22-2-2-222-2-2-22000000002-200000000-2-22200000000-2-222000000000000
χ272222-2-2-2-2222-22-2-2-2-2-222-2200000000-220000000022-2-200000000-2-222000000000000
χ282222-2-2-2-2222-22-2-2-2-2-222-2200000000-2200000000-2-2220000000022-2-2000000000000
χ292222-2-2-2-222-22-2-2-2222-2-22-222-2-222-2-2-2200000000000022-2-200000000000000000000
χ302222-2-2-2-222-22-2-2-2222-2-22-2-2-222-2-222-22000000000000-2-22200000000000000000000
χ312222-2-2-2-222-22-2-2-22-2-2222-222-2-222-2-22-2000000000000-2-22200000000000000000000
χ322222-2-2-2-222-22-2-2-22-2-2222-2-2-222-2-2222-200000000000022-2-200000000000000000000
χ332222-2-2-2-2-2-2-22-22220000-2222-2-2-2-2220000000000000000000000000002i−2i02i−2i000000
χ342222-2-2-2-2-2-2-22-22220000-2222-2-2-2-222000000000000000000000000000−2i2i0−2i2i000000
χ352222-2-2-2-2-2-2-22-22220000-22-2-22222-2-20000000000000000000000000002i−2i0−2i2i000000
χ362222-2-2-2-2-2-2-22-22220000-22-2-22222-2-2000000000000000000000000000−2i2i02i−2i000000
χ3722-2-22-2-222-20002-202-22-200i2−i2i2−i2i2−i2i2−i20000002i−2i002−22−2i2−i2i2−i2002i−2i2−22−2000000000000
χ3822-2-22-2-222-20002-202-22-200i2−i2i2−i2i2−i2i2−i2000000−2i2i00−22−22i2−i2i2−i200−2i2i−22−22000000000000
χ3922-2-22-2-222-20002-202-22-200−i2i2−i2i2−i2i2−i2i20000002i−2i00−22−22−i2i2−i2i2002i−2i−22−22000000000000
χ4022-2-22-2-222-20002-202-22-200−i2i2−i2i2−i2i2−i2i2000000−2i2i002−22−2−i2i2−i2i200−2i2i2−22−2000000000000
χ4122-2-22-2-222-20002-20-22-2200i2−i2i2−i2i2−i2i2−i20000002i−2i002−22−2−i2i2−i2i200−2i2i−22−22000000000000
χ4222-2-22-2-222-20002-20-22-2200i2−i2i2−i2i2−i2i2−i2000000−2i2i00−22−22−i2i2−i2i2002i−2i2−22−2000000000000
χ4322-2-22-2-222-20002-20-22-2200−i2i2−i2i2−i2i2−i2i20000002i−2i00−22−22i2−i2i2−i200−2i2i2−22−2000000000000
χ4422-2-22-2-222-20002-20-22-2200−i2i2−i2i2−i2i2−i2i2000000−2i2i002−22−2i2−i2i2−i2002i−2i−22−22000000000000
χ4522-2-2-222-22-2000-2202-2-2200i2−i2−i2i2i2−i2−i2i2002i−2i0000002−2−22i2−i2−i2i22i−2i002−2−22000000000000
χ4622-2-2-222-22-2000-2202-2-2200i2−i2−i2i2i2−i2−i2i200−2i2i000000−222−2i2−i2−i2i2−2i2i00−222−2000000000000
χ4722-2-2-222-22-2000-2202-2-2200−i2i2i2−i2−i2i2i2−i2002i−2i000000−222−2−i2i2i2−i22i−2i00−222−2000000000000
χ4822-2-2-222-22-2000-2202-2-2200−i2i2i2−i2−i2i2i2−i200−2i2i0000002−2−22−i2i2i2−i2−2i2i002−2−22000000000000
χ4922-2-2-222-22-2000-220-222-200i2−i2−i2i2i2−i2−i2i2002i−2i0000002−2−22−i2i2i2−i2−2i2i00−222−2000000000000
χ5022-2-2-222-22-2000-220-222-200i2−i2−i2i2i2−i2−i2i200−2i2i000000−222−2−i2i2i2−i22i−2i002−2−22000000000000
χ5122-2-2-222-22-2000-220-222-200−i2i2i2−i2−i2i2i2−i2002i−2i000000−222−2i2−i2−i2i2−2i2i002−2−22000000000000
χ5222-2-2-222-22-2000-220-222-200−i2i2i2−i2−i2i2i2−i200−2i2i0000002−2−22i2−i2−i2i22i−2i00−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44-4444-400004-40000000000000000000000000000000000000000000000
χ5544-4-44-4-44-44000-4400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ5644-4-44-4-44-44000-440000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ5744-4-4-444-4-440004-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5844-4-4-444-4-440004-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ594-4-444-44-4004-4-40040000000000000000004i−4i00000000000000000000000000000000
χ604-4-444-44-4004-4-4004000000000000000000−4i4i00000000000000000000000000000000
χ614-4-444-44-400-44400-400000000000000000000000000000000000000000000002i2−2i20000
χ624-4-444-44-400-44400-40000000000000000000000000000000000000000000000−2i22i20000
χ634-4-44-44-440044-400-40000000000000000000000000000000000000000000000002i2−2i200
χ644-4-44-44-440044-400-4000000000000000000000000000000000000000000000000−2i22i200
χ654-4-44-44-4400-4-4400400000000000000000000004-40000000000000000000000000000
χ664-4-44-44-4400-4-440040000000000000000000000-440000000000000000000000000000
χ678-88-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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