Finite Group Databasebeta

← Group #310183

Character table — Group #310183

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-111-111-1-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-111111111-1-1-1-11111-1-11-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-1
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
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111111-1-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111111111111-1-1-1-11-1-1-1-11
χ17222222222-222-2-2-2222220000-2-222220000-2-2002200-2-20000000000000000-20000000000
χ18222222222-222-2-2-2222220000-2-2-2-2-2-20000-2-200-2-20022000000000000000020000000000
χ19222222222-222-2-2-22-2-2-2-20000-2-2222200002200-2-200-2-2000000000000000020000000000
χ20222222222-222-2-2-22-2-2-2-20000-2-2-2-2-2-2000022002200220000000000000000-20000000000
χ2122222222-22-2-2222-200002222-2-20000222200-2-20022000000-2-2000000000000000-200000
χ2222222222-22-2-2222-200002222-2-20000-2-2-2-200-2-200-2-200000022000000000000000200000
χ2322222222-22-2-2222-20000-2-2-2-2-2-200002222002200-2-2000000-2-2000000000000000200000
χ2422222222-22-2-2222-20000-2-2-2-2-2-20000-2-2-2-20022002200000022000000000000000-200000
χ25222-2-22-2-2-202-200022i2i−2i−2i0000002i2i−2i−2i22−2−200002-20000i2i2−i2−i22−20000i2i2−i2−i2000000002−2000
χ26222-2-22-2-2-202-200022i2i−2i−2i0000002i2i−2i−2i−2−22200002-20000−i2−i2i2i2−220000−i2−i2i2i200000000−22000
χ27222-2-22-2-2-202-200022i2i−2i−2i000000−2i−2i2i2i22−2−20000-220000i2i2−i2−i22−20000−i2−i2i2i200000000−22000
χ28222-2-22-2-2-202-200022i2i−2i−2i000000−2i−2i2i2i−2−2220000-220000−i2−i2i2i2−220000i2i2−i2−i2000000002−2000
χ29222-2-22-2-2-202-20002−2i−2i2i2i0000002i2i−2i−2i22−2−20000-220000−i2−i2i2i22−20000i2i2−i2−i200000000−22000
χ30222-2-22-2-2-202-20002−2i−2i2i2i0000002i2i−2i−2i−2−2220000-220000i2i2−i2−i2−220000−i2−i2i2i2000000002−2000
χ31222-2-22-2-2-202-20002−2i−2i2i2i000000−2i−2i2i2i22−2−200002-20000−i2−i2i2i22−20000−i2−i2i2i2000000002−2000
χ32222-2-22-2-2-202-20002−2i−2i2i2i000000−2i−2i2i2i−2−22200002-20000i2i2−i2−i2−220000i2i2−i2−i200000000−22000
χ3322-2-2-2-22222-2-2-22-2200002i2i−2i−2i2-200000000002i−2i0000002-22-200000000000002i−2i00000000
χ3422-2-2-2-22222-2-2-22-2200002i2i−2i−2i2-200000000002i−2i000000-22-220000000000000−2i2i00000000
χ3522-2-2-2-22222-2-2-22-220000−2i−2i2i2i2-20000000000−2i2i0000002-22-20000000000000−2i2i00000000
χ3622-2-2-2-22222-2-2-22-220000−2i−2i2i2i2-20000000000−2i2i000000-22-2200000000000002i−2i00000000
χ3722-2-2-2-222-2222-22-2-22i−2i2i−2i2i2i−2i−2i-22000000002i−2i−2i2i000000000000000000002-200000000000
χ3822-2-2-2-222-2222-22-2-22i−2i2i−2i−2i−2i2i2i-22000000002i−2i2i−2i00000000000000000000-2200000000000
χ3922-2-2-2-222-2222-22-2-2−2i2i−2i2i2i2i−2i−2i-2200000000−2i2i−2i2i00000000000000000000-2200000000000
χ4022-2-2-2-222-2222-22-2-2−2i2i−2i2i−2i−2i2i2i-2200000000−2i2i2i−2i000000000000000000002-200000000000
χ4122-2-2-2-222-2-2222-22-22i−2i2i−2i00002-200000000−2i2i000000000000002i2i−2i−2i0000000002-2000000
χ4222-2-2-2-222-2-2222-22-22i−2i2i−2i00002-200000000−2i2i00000000000000−2i−2i2i2i000000000-22000000
χ4322-2-2-2-222-2-2222-22-2−2i2i−2i2i00002-2000000002i−2i000000000000002i2i−2i−2i000000000-22000000
χ4422-2-2-2-222-2-2222-22-2−2i2i−2i2i00002-2000000002i−2i00000000000000−2i−2i2i2i0000000002-2000000
χ452-222-2-22-20200-2-22000002-22-200i2−i2i2−i22i−2i2i−2i0000002i−2ii2−i2000000i2−i2i2−i22−22−200000000002−20
χ462-222-2-22-20200-2-22000002-22-200i2−i2i2−i2−2i2i−2i2i000000−2i2ii2−i2000000i2−i2i2−i2−22−220000000000−220
χ472-222-2-22-20200-2-22000002-22-200−i2i2−i2i22i−2i2i−2i0000002i−2i−i2i2000000−i2i2−i2i2−22−220000000000−220
χ482-222-2-22-20200-2-22000002-22-200−i2i2−i2i2−2i2i−2i2i000000−2i2i−i2i2000000−i2i2−i2i22−22−200000000002−20
χ492-222-2-22-20200-2-2200000-22-2200i2−i2i2−i22i−2i2i−2i000000−2i2ii2−i2000000−i2i2−i2i22−22−20000000000−220
χ502-222-2-22-20200-2-2200000-22-2200i2−i2i2−i2−2i2i−2i2i0000002i−2ii2−i2000000−i2i2−i2i2−22−2200000000002−20
χ512-222-2-22-20200-2-2200000-22-2200−i2i2−i2i22i−2i2i−2i000000−2i2i−i2i2000000i2−i2i2−i2−22−2200000000002−20
χ522-222-2-22-20200-2-2200000-22-2200−i2i2−i2i2−2i2i−2i2i0000002i−2i−i2i2000000i2−i2i2−i22−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-44-4-440-44000-4000000000000002222−22−2200000000000000−2222000000000000000000000
χ55444-4-44-4-440-44000-400000000000000−22−2222220000000000000022−22000000000000000000000
χ5644-444-4-4-4404-4000-44-4-44000000000000000000000000000000000000000000000000000
χ5744-444-4-4-4404-4000-4-444-4000000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-40-44000400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5944-444-4-4-4-40-4400040000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ6044-4-4-4-4444-4-4-44-44400000000-44000000000000000000000000000000000000000000000
χ614-444-4-44-40-40044-4000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ624-444-4-44-40-40044-400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ634-44-44-4-4400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ644-44-44-4-4400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ654-44-44-4-44000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ664-44-44-4-44000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ674-4-4-4444-404004-4-4000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ684-4-4-4444-404004-4-400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ694-4-4-4444-40-400-4440000000000000000000000000000000000022−22−222200000000000000000
χ704-4-4-4444-40-400-44400000000000000000000000000000000000−222222−2200000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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