Finite Group Databasebeta

← Group #351069

Character table — Group #351069

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444444444444488888888444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ121111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11111-111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11111-111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11111-1-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11111-1-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-222-2-2222-2-22222-2-2-2-2-2-200000000222-2-2-2000000000000000000000000
χ18222222222-2-222-2-2222-2-2-2-2-2-2-2-22222000000002-2-222-2000000000000000000000000
χ19222222222-2-222-2-22-2-2222222-2-2-2-2-2-200000000-2-2-2222000000000000000000000000
χ20222222222-2-222-2-22-2-222-2-2-2-2-2-2222200000000-222-2-22000000000000000000000000
χ2122222222-222-2-222-222220000-2-2000022222222-20000-2-2-2-2-200000000000000000000
χ2222222222-222-2-222-222220000-2-20000-2-2-2-2-2-2-2-2-20000-2222200000000000000000000
χ2322222222-222-2-222-2-2-2-2-20000-2-200002222-2-2-2-2200002-2-22200000000000000000000
χ2422222222-222-2-222-2-2-2-2-20000-2-20000-2-2-2-2222220000222-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2000022000000000000-20000200002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2000022000000000000-2000020000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22200002200000000000020000-200002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22200002200000000000020000-20000−2i−2i2i2i2i2i−2i−2i000000000000
χ292222-2-2-2-202200-2-202-22-2000000000022-2-222-2-20000000000000000002−22−22−22−20000
χ302222-2-2-2-202200-2-202-22-2000000000022-2-222-2-2000000000000000000−22−22−22−220000
χ312222-2-2-2-202200-2-202-22-20000000000-2-222-2-2220000000000000000002−22−2−22−220000
χ322222-2-2-2-202200-2-202-22-20000000000-2-222-2-222000000000000000000−22−222−22−20000
χ332222-2-2-2-202200-2-20-22-22000000000022-2-2-2-2220000000000000000002−2−222−2−220000
χ342222-2-2-2-202200-2-20-22-22000000000022-2-2-2-222000000000000000000−222−2−222−20000
χ352222-2-2-2-202200-2-20-22-220000000000-2-22222-2-20000000000000000002−2−22−222−20000
χ362222-2-2-2-202200-2-20-22-220000000000-2-22222-2-2000000000000000000−222−22−2−220000
χ3722-2-2-222-222-2-2-22-2200002i2i−2i−2i2-22i2i−2i−2i00002i−2i2i−2i000000002i−2i00002-22-2000000000000
χ3822-2-2-222-222-2-2-22-2200002i2i−2i−2i2-22i2i−2i−2i0000−2i2i−2i2i00000000−2i2i0000-22-22000000000000
χ3922-2-2-222-222-2-2-22-220000−2i−2i2i2i2-2−2i−2i2i2i00002i−2i2i−2i000000002i−2i0000-22-22000000000000
χ4022-2-2-222-222-2-2-22-220000−2i−2i2i2i2-2−2i−2i2i2i0000−2i2i−2i2i00000000−2i2i00002-22-2000000000000
χ4122-2-2-222-22-22-2-2-22200002i2i−2i−2i-22−2i−2i2i2i2i−2i2i−2i00000000002i−2i002-22-20000000000000000
χ4222-2-2-222-22-22-2-2-22200002i2i−2i−2i-22−2i−2i2i2i−2i2i−2i2i0000000000−2i2i00-22-220000000000000000
χ4322-2-2-222-22-22-2-2-2220000−2i−2i2i2i-222i2i−2i−2i2i−2i2i−2i00000000002i−2i00-22-220000000000000000
χ4422-2-2-222-22-22-2-2-2220000−2i−2i2i2i-222i2i−2i−2i−2i2i−2i2i0000000000−2i2i002-22-20000000000000000
χ4522-2-2-222-2-22-2222-2-200000000-22000000002i−2i2i−2i02-22-2000−2i2i2i−2i−2i2i0000000000000000
χ4622-2-2-222-2-22-2222-2-200000000-22000000002i−2i2i−2i0-22-22000−2i2i−2i2i2i−2i0000000000000000
χ4722-2-2-222-2-22-2222-2-200000000-2200000000−2i2i−2i2i02-22-20002i−2i−2i2i2i−2i0000000000000000
χ4822-2-2-222-2-22-2222-2-200000000-2200000000−2i2i−2i2i0-22-220002i−2i2i−2i−2i2i0000000000000000
χ4922-2-2-222-2-2-2222-22-2000000002-200002i−2i2i−2i000002-2-220−2i2i000000−2i2i2i−2i000000000000
χ5022-2-2-222-2-2-2222-22-2000000002-200002i−2i2i−2i00000-222-20−2i2i0000002i−2i−2i2i000000000000
χ5122-2-2-222-2-2-2222-22-2000000002-20000−2i2i−2i2i000002-2-2202i−2i0000002i−2i−2i2i000000000000
χ5222-2-2-222-2-2-2222-22-2000000002-20000−2i2i−2i2i00000-222-202i−2i000000−2i2i2i−2i000000000000
χ534444-4-4-4-40-4-4004404-4-44000000000000000000000000000000000000000000000000
χ544444-4-4-4-40-4-400440-444-4000000000000000000000000000000000000000000000000
χ5544-4-44-4-4404-400-4400000000000000000004i−4i−4i4i000000000000000000000000000000
χ5644-4-44-4-4404-400-440000000000000000000−4i4i4i−4i000000000000000000000000000000
χ5744-4-44-4-440-44004-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ5844-4-44-4-440-44004-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ594-44-444-4-44004-400-400004-44-400000000000000000000000000000000000000000000
χ604-44-444-4-44004-400-40000-44-4400000000000000000000000000000000000000000000
χ614-44-444-4-4-400-4400400000000004i−4i4i−4i00000000000000000000000000000000000000
χ624-44-444-4-4-400-440040000000000−4i4i−4i4i00000000000000000000000000000000000000
χ634-4-44-44-44400-4400-400004i−4i−4i4i00000000000000000000000000000000000000000000
χ644-4-44-44-44400-4400-40000−4i4i4i−4i00000000000000000000000000000000000000000000
χ654-4-44-44-44-4004-400400000000004-4-4400000000000000000000000000000000000000
χ664-4-44-44-44-4004-40040000000000-444-400000000000000000000000000000000000000
χ678-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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