Finite Group Databasebeta

← Group #324992

Character table — Group #324992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444444444888844448888888888888888888888888844882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ10111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11-1-11
χ17222222222-2-222-2-22-2-222-2-222-2-2000022-2-2000000000000000000000000002-2000000
χ18222222222-2-222-2-22-2-222-2-222-2-20000-2-22200000000000000000000000000-22000000
χ19222222222-2-222-2-22-2-2-2-222-2-222000022-2-200000000000000000000000000-22000000
χ20222222222-2-222-2-22-2-2-2-222-2-2220000-2-222000000000000000000000000002-2000000
χ2122222222-222-2-222-2-2-222-2-2-2-22222220000-2-20000000022-2-200000000000000000000
χ2222222222-222-2-222-2-2-222-2-2-2-222-2-2-2-200002200000000-2-22200000000000000000000
χ2322222222-222-2-222-2-2-2-2-22222-2-222220000-2-200000000-2-22200000000000000000000
χ2422222222-222-2-222-2-2-2-2-22222-2-2-2-2-2-20000220000000022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2-2-200000000000000000000002i2i−2i−2i00000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000000000−2i−2i2i2i0000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000002i2i−2i−2i0000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000−2i−2i2i2i00000000002i−2i0000
χ29222-2-22-2-22-2-2-2-22222-2000000002i2i−2i−2i00002i−2i2i2i−2i−2i000000000000000022-2-200000000
χ30222-2-22-2-22-2-2-2-22222-2000000002i2i−2i−2i00002i−2i−2i−2i2i2i0000000000000000-2-22200000000
χ31222-2-22-2-22-2-2-2-22222-200000000−2i−2i2i2i0000−2i2i2i2i−2i−2i0000000000000000-2-22200000000
χ32222-2-22-2-22-2-2-2-22222-200000000−2i−2i2i2i0000−2i2i−2i−2i2i2i000000000000000022-2-200000000
χ33222-2-22-2-2-2-2-22222-2-22000000002i2i−2i−2i0000−2i2i000022-2-2000000002i2i−2i−2i000000000000
χ34222-2-22-2-2-2-2-22222-2-22000000002i2i−2i−2i0000−2i2i0000-2-22200000000−2i−2i2i2i000000000000
χ35222-2-22-2-2-2-2-22222-2-2200000000−2i−2i2i2i00002i−2i000022-2-200000000−2i−2i2i2i000000000000
χ36222-2-22-2-2-2-2-22222-2-2200000000−2i−2i2i2i00002i−2i0000-2-222000000002i2i−2i−2i000000000000
χ3722-22-2-22-202-2002-2000002i−2i2i−2i002-22-2000000i2−i2i2−i22−22−2002i−2i00002−22−2i2−i2i2−i200000000
χ3822-22-2-22-202-2002-2000002i−2i2i−2i002-22-2000000−i2i2−i2i2−22−22002i−2i0000−22−22−i2i2−i2i200000000
χ3922-22-2-22-202-2002-2000002i−2i2i−2i00-22-22000000i2−i2i2−i2−22−2200−2i2i00002−22−2−i2i2−i2i200000000
χ4022-22-2-22-202-2002-2000002i−2i2i−2i00-22-22000000−i2i2−i2i22−22−200−2i2i0000−22−22i2−i2i2−i200000000
χ4122-22-2-22-202-2002-200000−2i2i−2i2i002-22-2000000i2−i2i2−i2−22−2200−2i2i0000−22−22i2−i2i2−i200000000
χ4222-22-2-22-202-2002-200000−2i2i−2i2i002-22-2000000−i2i2−i2i22−22−200−2i2i00002−22−2−i2i2−i2i200000000
χ4322-22-2-22-202-2002-200000−2i2i−2i2i00-22-22000000i2−i2i2−i22−22−2002i−2i0000−22−22−i2i2−i2i200000000
χ4422-22-2-22-202-2002-200000−2i2i−2i2i00-22-22000000−i2i2−i2i2−22−22002i−2i00002−22−2i2−i2i2−i200000000
χ4522-2-22-2-220-22002-20002i−2i00002i−2i2i−2i−2i2i0000002−2−222−2−222-2000000i2−i2−i2i2−i2i2i2−i200000000
χ4622-2-22-2-220-22002-20002i−2i00002i−2i2i−2i−2i2i000000−222−2−222−22-2000000−i2i2i2−i2i2−i2−i2i200000000
χ4722-2-22-2-220-22002-20002i−2i00002i−2i−2i2i2i−2i0000002−2−22−222−2-22000000i2−i2−i2i2i2−i2−i2i200000000
χ4822-2-22-2-220-22002-20002i−2i00002i−2i−2i2i2i−2i000000−222−22−2−22-22000000−i2i2i2−i2−i2i2i2−i200000000
χ4922-2-22-2-220-22002-2000−2i2i0000−2i2i2i−2i−2i2i0000002−2−22−222−2-22000000−i2i2i2−i2−i2i2i2−i200000000
χ5022-2-22-2-220-22002-2000−2i2i0000−2i2i2i−2i−2i2i000000−222−22−2−22-22000000i2−i2−i2i2i2−i2−i2i200000000
χ5122-2-22-2-220-22002-2000−2i2i0000−2i2i−2i2i2i−2i0000002−2−222−2−222-2000000−i2i2i2−i2i2−i2−i2i200000000
χ5222-2-22-2-220-22002-2000−2i2i0000−2i2i−2i2i2i−2i000000−222−2−222−22-2000000i2−i2−i2i2−i2i2i2−i200000000
χ53444-4-44-4-4444-4-4-4-44-4400000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-44444-4-4-44-400000000000000000000000000000000000000000000000000
χ5544-44-4-44-40-4400-44000004i−4i−4i4i00000000000000000000000000000000000000000000
χ5644-44-4-44-40-4400-4400000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5744-4-44-4-4404-400-440004i−4i0000−4i4i000000000000000000000000000000000000000000
χ5844-4-44-4-4404-400-44000−4i4i00004i−4i000000000000000000000000000000000000000000
χ594-4-44-44-444004-400-4000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ604-4-44-44-444004-400-400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ614-4-44-44-44-400-440040000000000000000000000000000000022−22−22220000000000000000
χ624-4-44-44-44-400-4400400000000000000000000000000000000−222222−220000000000000000
χ634-4-4-4444-4400-4400-400000000000000004i−4i0000000000000000000000000000000000
χ644-4-4-4444-4400-4400-40000000000000000−4i4i0000000000000000000000000000000000
χ654-4-4-4444-4-4004-4004000000000000004-4000000000000000000000000000000000000
χ664-4-4-4444-4-4004-400400000000000000-44000000000000000000000000000000000000
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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