Finite Group Databasebeta

← Group #308125

Character table — Group #308125

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-11-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111111111-1-11111-1-1-1-1-1-11
χ17222222222-2-2222-2-22222-20000-222220000-2-2002200-2-20000000000000000000-20000000
χ18222222222-2-2222-2-22222-20000-2-2-2-2-20000-2-200-2-20022000000000000000000020000000
χ19222222222-2-2222-2-2-2-2-2-2-20000-2222200002200-2-200-2-2000000000000000000020000000
χ20222222222-2-2222-2-2-2-2-2-2-20000-2-2-2-2-2000022002200220000000000000000000-20000000
χ2122222222-222-2-2-2220000-22222-20000222200-2-20022000000-2-20000000000-20000000000
χ2222222222-222-2-2-2220000-22222-20000-2-2-2-200-2-200-2-200000022000000000020000000000
χ2322222222-222-2-2-2220000-2-2-2-2-2-200002222002200-2-2000000-2-2000000000020000000000
χ2422222222-222-2-2-2220000-2-2-2-2-2-20000-2-2-2-200220022000000220000000000-20000000000
χ25222-22-2-2-2222-22-2-2-222-2-220000-2000000002-20000000022-2-200000000002-200000000000
χ26222-22-2-2-2222-22-2-2-222-2-220000-2000000002-200000000-2-2220000000000-2200000000000
χ27222-22-2-2-2222-22-2-2-2-2-22220000-200000000-220000000022-2-20000000000-2200000000000
χ28222-22-2-2-2222-22-2-2-2-2-22220000-200000000-2200000000-2-22200000000002-200000000000
χ29222-22-2-2-22-2-2-22-22222-2-2-22i2i−2i−2i200000000-222i−2i000000000000000000000002i−2i00000000
χ30222-22-2-2-22-2-2-22-22222-2-2-2−2i−2i2i2i200000000-22−2i2i00000000000000000000000−2i2i00000000
χ31222-22-2-2-22-2-2-22-222-2-222-22i2i−2i−2i2000000002-22i−2i00000000000000000000000−2i2i00000000
χ32222-22-2-2-22-2-2-22-222-2-222-2−2i−2i2i2i2000000002-2−2i2i000000000000000000000002i−2i00000000
χ33222-22-2-2-2-2-2-22-2222000022i2i−2i−2i-20000000000−2i2i00000000000022-2-200000000002i−2i00000
χ34222-22-2-2-2-2-2-22-2222000022i2i−2i−2i-20000000000−2i2i000000000000-2-2220000000000−2i2i00000
χ35222-22-2-2-2-2-2-22-222200002−2i−2i2i2i-200000000002i−2i00000000000022-2-20000000000−2i2i00000
χ36222-22-2-2-2-2-2-22-222200002−2i−2i2i2i-200000000002i−2i000000000000-2-22200000000002i−2i00000
χ3722-22-2-22-2-20022-2002-22-20000002i2i−2i−2ii2i2−i2−i200002i−2i00000000i2−i2i2−i2i2−i222−2−2000000002−2000
χ3822-22-2-22-2-20022-2002-22-20000002i2i−2i−2i−i2−i2i2i200002i−2i00000000−i2i2−i2i2−i2i2−2−22200000000−22000
χ3922-22-2-22-2-20022-2002-22-2000000−2i−2i2i2ii2i2−i2−i20000−2i2i00000000i2−i2i2−i2i2−i2−2−22200000000−22000
χ4022-22-2-22-2-20022-2002-22-2000000−2i−2i2i2i−i2−i2i2i20000−2i2i00000000−i2i2−i2i2−i2i222−2−2000000002−2000
χ4122-22-2-22-2-20022-200-22-220000002i2i−2i−2ii2i2−i2−i20000−2i2i00000000i2−i2−i2i2−i2i222−2−200000000−22000
χ4222-22-2-22-2-20022-200-22-220000002i2i−2i−2i−i2−i2i2i20000−2i2i00000000−i2i2i2−i2i2−i2−2−222000000002−2000
χ4322-22-2-22-2-20022-200-22-22000000−2i−2i2i2ii2i2−i2−i200002i−2i00000000i2−i2−i2i2−i2i2−2−222000000002−2000
χ4422-22-2-22-2-20022-200-22-22000000−2i−2i2i2i−i2−i2i2i200002i−2i00000000−i2i2i2−i2i2−i222−2−200000000−22000
χ452-2-2222-2-202-20002-2000002i−2i2i−2i0i2−i2i2−i22-22-20000002i−2ii2−i22−22−2000000i2−i2i2−i200000000002−20
χ462-2-2222-2-202-20002-2000002i−2i2i−2i0i2−i2i2−i2-22-22000000−2i2ii2−i22−22−2000000−i2i2−i2i20000000000−220
χ472-2-2222-2-202-20002-2000002i−2i2i−2i0−i2i2−i2i22-22-20000002i−2i−i2i2−22−22000000−i2i2−i2i20000000000−220
χ482-2-2222-2-202-20002-2000002i−2i2i−2i0−i2i2−i2i2-22-22000000−2i2i−i2i2−22−22000000i2−i2i2−i200000000002−20
χ492-2-2222-2-202-20002-200000−2i2i−2i2i0i2−i2i2−i22-22-2000000−2i2ii2−i2−22−22000000i2−i2i2−i20000000000−220
χ502-2-2222-2-202-20002-200000−2i2i−2i2i0i2−i2i2−i2-22-220000002i−2ii2−i2−22−22000000−i2i2−i2i200000000002−20
χ512-2-2222-2-202-20002-200000−2i2i−2i2i0−i2i2−i2i22-22-2000000−2i2i−i2i22−22−2000000−i2i2−i2i200000000002−20
χ522-2-2222-2-202-20002-200000−2i2i−2i2i0−i2i2−i2i2-22-220000002i−2i−i2i22−22−2000000i2−i2i2−i20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4444-44-4-40000-400004000000000000000000000000000000000000000000000
χ5544-44-4-44-4400-4-4400000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ5644-44-4-44-4400-4-440000000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ5744-4-4-44-444004-4-40000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5844-4-4-44-444004-4-4000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5944-4-4-44-44-400-444004-4-44000000000000000000000000000000000000000000000000000
χ6044-4-4-44-44-400-44400-444-4000000000000000000000000000000000000000000000000000
χ614-444-4-4-4400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ624-444-4-4-4400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ634-444-4-4-44000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ644-444-4-4-44000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ654-4-4444-4-40-44000-4400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ664-4-4444-4-40-44000-440000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ674-4-4-44-44404-4000-44000000000000000000000000000022−22−222200000000000000000000000
χ684-4-4-44-44404-4000-440000000000000000000000000000−222222−2200000000000000000000000
χ694-4-4-44-4440-440004-4000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-44-4440-440004-400000-444-40000000000000000000000000000000000000000000000
χ718-88-8-888-8000000000000000000000000000000000000000000000000000000000000000

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