Finite Group Databasebeta

← Group #308129

Character table — Group #308129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1111111111111-1-11-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-111-1-1111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-111-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11111-1-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-11111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11-1-1111-1-1-1-11
χ17222222222-2-2222-2-22222-20000-222220000-2-20000220000-2-2000000000000-20000000000
χ18222222222-2-2222-2-22222-20000-2-2-2-2-20000-2-20000-2-200002200000000000020000000000
χ19222222222-2-2222-2-2-2-2-2-2-20000-222220000220000-2-20000-2-200000000000020000000000
χ20222222222-2-2222-2-2-2-2-2-2-20000-2-2-2-2-2000022000022000022000000000000-20000000000
χ2122222222-222-2-2-2220000-22222-20000222200-2-22200000000-2-2000000000000000-200000
χ2222222222-222-2-2-2220000-22222-20000-2-2-2-200-2-2-2-20000000022000000000000000200000
χ2322222222-222-2-2-2220000-2-2-2-2-2-2000022220022-2-200000000-2-2000000000000000200000
χ2422222222-222-2-2-2220000-2-2-2-2-2-20000-2-2-2-20022220000000022000000000000000-200000
χ25222-2-22-2-2-200-2220022-2-20000002i2i−2i−2i22−2−20000002i−2i0000002−222−2−2i2i2−i2−i200000000i2−i2000
χ26222-2-22-2-2-200-2220022-2-20000002i2i−2i−2i−2−2220000002i−2i000000−22−2−222−i2−i2i2i200000000−i2i2000
χ27222-2-22-2-2-200-2220022-2-2000000−2i−2i2i2i22−2−2000000−2i2i0000002−222−2−2−i2−i2i2i200000000−i2i2000
χ28222-2-22-2-2-200-2220022-2-2000000−2i−2i2i2i−2−222000000−2i2i000000−22−2−222i2i2−i2−i200000000i2−i2000
χ29222-2-22-2-2-200-22200-2-2220000002i2i−2i−2i22−2−2000000−2i2i0000002−2−2−222i2i2−i2−i200000000−i2i2000
χ30222-2-22-2-2-200-22200-2-2220000002i2i−2i−2i−2−222000000−2i2i000000−2222−2−2−i2−i2i2i200000000i2−i2000
χ31222-2-22-2-2-200-22200-2-222000000−2i−2i2i2i22−2−20000002i−2i0000002−2−2−222−i2−i2i2i200000000i2−i2000
χ32222-2-22-2-2-200-22200-2-222000000−2i−2i2i2i−2−2220000002i−2i000000−2222−2−2i2i2−i2−i200000000−i2i2000
χ3322-2-22-22-202-20002-2000002i2i−2i−2i0i2−i2i2−i22i−2i2i−2i00002-20022−2−2i2−i20000002−22−20000000000i2−i20
χ3422-2-22-22-202-20002-2000002i2i−2i−2i0i2−i2i2−i2−2i2i−2i2i0000-220022−2−2i2−i2000000−22−220000000000−i2i20
χ3522-2-22-22-202-20002-2000002i2i−2i−2i0−i2i2−i2i22i−2i2i−2i00002-200−2−222−i2i2000000−22−220000000000−i2i20
χ3622-2-22-22-202-20002-2000002i2i−2i−2i0−i2i2−i2i2−2i2i−2i2i0000-2200−2−222−i2i20000002−22−20000000000i2−i20
χ3722-2-22-22-202-20002-200000−2i−2i2i2i0i2−i2i2−i22i−2i2i−2i0000-2200−2−222i2−i20000002−22−20000000000−i2i20
χ3822-2-22-22-202-20002-200000−2i−2i2i2i0i2−i2i2−i2−2i2i−2i2i00002-200−2−222i2−i2000000−22−220000000000i2−i20
χ3922-2-22-22-202-20002-200000−2i−2i2i2i0−i2i2−i2i22i−2i2i−2i0000-220022−2−2−i2i2000000−22−220000000000i2−i20
χ4022-2-22-22-202-20002-200000−2i−2i2i2i0−i2i2−i2i2−2i2i−2i2i00002-20022−2−2−i2i20000002−22−20000000000−i2i20
χ412-2222-2-2-2222-22-2-2-22-22-220000-2000000002-20000002-22-20000000000002-200000000000
χ422-2222-2-2-2222-22-2-2-22-22-220000-2000000002-2000000-22-22000000000000-2200000000000
χ432-2222-2-2-2222-22-2-2-2-22-2220000-200000000-220000002-22-2000000000000-2200000000000
χ442-2222-2-2-2222-22-2-2-2-22-2220000-200000000-22000000-22-220000000000002-200000000000
χ452-2222-2-2-22-2-2-22-2222-22-2-22i−2i2i−2i200000000-222i−2i00000000000000000000000002i−2i000000
χ462-2222-2-2-22-2-2-22-2222-22-2-2−2i2i−2i2i200000000-22−2i2i0000000000000000000000000−2i2i000000
χ472-2222-2-2-22-2-2-22-222-22-22-22i−2i2i−2i2000000002-22i−2i0000000000000000000000000−2i2i000000
χ482-2222-2-2-22-2-2-22-222-22-22-2−2i2i−2i2i2000000002-2−2i2i00000000000000000000000002i−2i000000
χ492-2222-2-2-2-2-2-22-2222000022i−2i2i−2i-20000000000−2i2i0000000000002-22-200000002i−2i00000000
χ502-2222-2-2-2-2-2-22-2222000022i−2i2i−2i-20000000000−2i2i000000000000-22-220000000−2i2i00000000
χ512-2222-2-2-2-2-2-22-222200002−2i2i−2i2i-200000000002i−2i0000000000002-22-20000000−2i2i00000000
χ522-2222-2-2-2-2-2-22-222200002−2i2i−2i2i-200000000002i−2i000000000000-22-2200000002i−2i00000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-44-4-44004-4-400000000000000002222−22−2200000000000000−2222000000000000000000000
χ55444-4-44-4-44004-4-40000000000000000−22−2222220000000000000022−22000000000000000000000
χ5644-44-4-4-4400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ5744-44-4-4-4400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ5844-44-4-4-44000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ5944-44-4-4-44000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ6044-4-44-44-40-44000-4400000000002i2−2i22i2−2i20000000000000000−2i22i200000000000000000000000
χ6144-4-44-44-40-44000-440000000000−2i22i2−2i22i200000000000000002i2−2i200000000000000000000000
χ624-4444-4-4-4-4444-44-4-40000-400004000000000000000000000000000000000000000000000
χ634-44-4-4-444400-4-4400000000000000000000000000000000000022−22−222200000000000000000
χ644-44-4-4-444400-4-44000000000000000000000000000000000000−222222−2200000000000000000
χ654-44-4-4-444-40044-4004-4-44000000000000000000000000000000000000000000000000000
χ664-44-4-4-444-40044-400-444-4000000000000000000000000000000000000000000000000000
χ674-4-4-444-4404-4000-440000000000000000000000000022−22−22220000000000000000000000000
χ684-4-4-444-4404-4000-4400000000000000000000000000−222222−220000000000000000000000000
χ694-4-4-444-440-440004-4000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-444-440-440004-400000-444-40000000000000000000000000000000000000000000000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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