Finite Group Databasebeta

← Group #288839

Character table — Group #288839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888822224444444488888888888888888844882244
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-1
χ10111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-11-11
χ11111111111111111111-1-1-1-111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-11
χ12111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111111111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-11-1-11
χ17222222222-2-2222-2-2-2-222220000000022220000-2-2-2-20000-2-200000000000000000000
χ18222222222-2-2222-2-2-2-2222200000000-2-2-2-2000022220000-2-200000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-20000000022-2-20000-2-22200002200000000000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-200000000-2-222000022-2-200002200000000000000000000
χ2122222222-222-2-2-222-2-200002222-2-2-2-2000022-2-200000000000000000000002-2000000
χ2222222222-222-2-2-222-2-200002222-2-2-2-20000-2-2220000000000000000000000-22000000
χ2322222222-222-2-2-222-2-20000-2-2-2-22222000022-2-20000000000000000000000-22000000
χ2422222222-222-2-2-222-2-20000-2-2-2-222220000-2-22200000000000000000000002-2000000
χ252222-2-2-2-2-20022-2000022-2-2i2i2−i2−i2i2i2−i2−i22-22-200000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ262222-2-2-2-2-20022-2000022-2-2i2i2−i2−i2i2i2−i2−i2-22-2200000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ272222-2-2-2-2-20022-2000022-2-2−i2−i2i2i2−i2−i2i2i22-22-200000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ282222-2-2-2-2-20022-2000022-2-2−i2−i2i2i2−i2−i2i2i2-22-2200000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ292222-2-2-2-2-20022-20000-2-222i2i2−i2−i2i2i2−i2−i22-2-2200000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ302222-2-2-2-2-20022-20000-2-222i2i2−i2−i2i2i2−i2−i2-222-200000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ312222-2-2-2-2-20022-20000-2-222−i2−i2i2i2−i2−i2i2i22-2-2200000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ322222-2-2-2-2-20022-20000-2-222−i2−i2i2i2−i2−i2i2i2-222-200000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ3322-2-22-2-22222-22-2-2-2-2200002i−2i2i−2i2i−2i2i−2i00000000000022-2-200000000000000002i−2i0000
χ3422-2-22-2-22222-22-2-2-2-2200002i−2i2i−2i2i−2i2i−2i000000000000-2-2220000000000000000−2i2i0000
χ3522-2-22-2-22222-22-2-2-2-220000−2i2i−2i2i−2i2i−2i2i00000000000022-2-20000000000000000−2i2i0000
χ3622-2-22-2-22222-22-2-2-2-220000−2i2i−2i2i−2i2i−2i2i000000000000-2-22200000000000000002i−2i0000
χ3722-2-22-2-22-2222-22-2-22-22-22-22i−2i2i−2i−2i2i−2i2i00000000000000002-2000000002i−2i2i−2i00000000
χ3822-2-22-2-22-2222-22-2-22-22-22-2−2i2i−2i2i2i−2i2i−2i00000000000000002-200000000−2i2i−2i2i00000000
χ3922-2-22-2-22-2222-22-2-22-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000-2200000000−2i2i−2i2i00000000
χ4022-2-22-2-22-2222-22-2-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000-22000000002i−2i2i−2i00000000
χ4122-2-22-2-22-2-2-22-2222-222-22-2000000000000000000000000-222-22-22-22-2000000000000
χ4222-2-22-2-22-2-2-22-2222-222-22-2000000000000000000000000-22-22-22-22-22000000000000
χ4322-2-22-2-22-2-2-22-2222-22-22-220000000000000000000000002-22-22-2-22-22000000000000
χ4422-2-22-2-22-2-2-22-2222-22-22-220000000000000000000000002-2-22-222-22-2000000000000
χ4522-2-2-222-22002-2-200002-2-222−2−22−222−2000000002i−2i2i−2i000000i2−i2−i2i2i2−i2−i2i22−2−2200000000
χ4622-2-2-222-22002-2-200002-2-222−2−22−222−200000000−2i2i−2i2i000000−i2i2i2−i2−i2i2i2−i22−2−2200000000
χ4722-2-2-222-22002-2-200002-2-22−222−22−2−22000000002i−2i2i−2i000000−i2i2i2−i2−i2i2i2−i2−222−200000000
χ4822-2-2-222-22002-2-200002-2-22−222−22−2−2200000000−2i2i−2i2i000000i2−i2−i2i2i2−i2−i2i2−222−200000000
χ4922-2-2-222-22002-2-20000-222-22−2−22−222−2000000002i−2i−2i2i000000i2−i2−i2i2−i2i2i2−i2−222−200000000
χ5022-2-2-222-22002-2-20000-222-22−2−22−222−200000000−2i2i2i−2i000000−i2i2i2−i2i2−i2−i2i2−222−200000000
χ5122-2-2-222-22002-2-20000-222-2−222−22−2−22000000002i−2i−2i2i000000−i2i2i2−i2i2−i2−i2i22−2−2200000000
χ5222-2-2-222-22002-2-20000-222-2−222−22−2−2200000000−2i2i2i−2i000000i2−i2−i2i2−i2i2i2−i22−2−2200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4400-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ554444-4-4-4-4400-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-4-44-4-444-4-4-44-4444-400000000000000000000000000000000000000000000000000
χ5744-4-4-444-4-400-4440000000022−22−222222−22−222200000000000000000000000000000000000000
χ5844-4-4-444-4-400-44400000000−222222−22−222222−2200000000000000000000000000000000000000
χ594-44-4-44-4404-40004-40000000000000000000000000022−2222−220000000000000000000000
χ604-44-4-44-4404-40004-400000000000000000000000000−2222−22220000000000000000000000
χ614-44-4-44-440-44000-440000000000000000004-400000000000000000000000000000000
χ624-44-4-44-440-44000-44000000000000000000-4400000000000000000000000000000000
χ634-4-44-4-44404-4000-440000000000000000000000000022−22−22220000000000000000000000
χ644-4-44-4-44404-4000-4400000000000000000000000000−222222−220000000000000000000000
χ654-4-44-4-4440-440004-4000000000000000000004-4000000000000000000000000000000
χ664-4-44-4-4440-440004-400000000000000000000-44000000000000000000000000000000
χ678-88-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8888-8-8000000000000000000000000000000000000000000000000000000000000

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