Finite Group Databasebeta

← Group #306331

Character table — Group #306331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882222444488888888888888884444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-111-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-11111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-111-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111111-1-11-1-1-1-1-1-11
χ17222222222-22-22-22-2-222220000-222220000-2-2220000-2-200000000000000-2000000000000
χ18222222222-22-22-22-2-222220000-2-2-2-2-20000-2-2-2-2000022000000000000002000000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-22222000022-2-20000-2-2000000000000002000000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-2-2-2-2-20000222200002200000000000000-2000000000000
χ2122222222-22-22-22-22-200002222-200002222000022-2-200-2-200000000000000000-20000000
χ2222222222-22-22-22-22-200002222-20000-2-2-2-20000-2-2-2-200220000000000000000020000000
χ2322222222-22-22-22-22-20000-2-2-2-2-2000022220000-2-22200-2-20000000000000000020000000
χ2422222222-22-22-22-22-20000-2-2-2-2-20000-2-2-2-200002222002200000000000000000-20000000
χ25222-22-2-2-22-2-222-2-22-200002i2i−2i−2i2000000000000002i−2i0000000022-2-200000000002i−2i00000
χ26222-22-2-2-22-2-222-2-22-200002i2i−2i−2i2000000000000002i−2i00000000-2-2220000000000−2i2i00000
χ27222-22-2-2-22-2-222-2-22-20000−2i−2i2i2i200000000000000−2i2i0000000022-2-20000000000−2i2i00000
χ28222-22-2-2-22-2-222-2-22-20000−2i−2i2i2i200000000000000−2i2i00000000-2-22200000000002i−2i00000
χ29222-22-2-2-2-222-2-222-2-222-2-200002000000002-200000000002i2i−2i−2i000000000002i−2i00000000
χ30222-22-2-2-2-222-2-222-2-222-2-200002000000002-20000000000−2i−2i2i2i00000000000−2i2i00000000
χ31222-22-2-2-2-222-2-222-2-2-2-2220000200000000-2200000000002i2i−2i−2i00000000000−2i2i00000000
χ32222-22-2-2-2-222-2-222-2-2-2-2220000200000000-220000000000−2i−2i2i2i000000000002i−2i00000000
χ33222-22-2-2-2-2-222-2-222222-2-22i2i−2i−2i-200000000-220000−2i2i000000000000000002i−2i0000000000
χ34222-22-2-2-2-2-222-2-222222-2-2−2i−2i2i2i-200000000-2200002i−2i00000000000000000−2i2i0000000000
χ35222-22-2-2-2-2-222-2-2222-2-2222i2i−2i−2i-2000000002-20000−2i2i00000000000000000−2i2i0000000000
χ36222-22-2-2-2-2-222-2-2222-2-222−2i−2i2i2i-2000000002-200002i−2i000000000000000002i−2i0000000000
χ3722-22-22-2-2-202020-2002i−2i2i−2i000002i2i−2i−2ii2i2−i2−i2002-2000000i2−i200002−22−222−2−200000000i2−i2000
χ3822-22-22-2-2-202020-2002i−2i2i−2i000002i2i−2i−2i−i2−i2i2i2002-2000000−i2i20000−22−22−2−22200000000−i2i2000
χ3922-22-22-2-2-202020-2002i−2i2i−2i00000−2i−2i2i2ii2i2−i2−i200-22000000i2−i200002−22−2−2−22200000000−i2i2000
χ4022-22-22-2-2-202020-2002i−2i2i−2i00000−2i−2i2i2i−i2−i2i2i200-22000000−i2i20000−22−2222−2−200000000i2−i2000
χ4122-22-22-2-2-202020-200−2i2i−2i2i000002i2i−2i−2ii2i2−i2−i200-22000000i2−i20000−22−2222−2−200000000−i2i2000
χ4222-22-22-2-2-202020-200−2i2i−2i2i000002i2i−2i−2i−i2−i2i2i200-22000000−i2i200002−22−2−2−22200000000i2−i2000
χ4322-22-22-2-2-202020-200−2i2i−2i2i00000−2i−2i2i2ii2i2−i2−i2002-2000000i2−i20000−22−22−2−22200000000i2−i2000
χ4422-22-22-2-2-202020-200−2i2i−2i2i00000−2i−2i2i2i−i2−i2i2i2002-2000000−i2i200002−22−222−2−200000000−i2i2000
χ452-2-222-22-202020-20-2000002i−2i2i−2i02−22−22i−2i2i−2i00002-2002−200i2−i2i2−i20000i2−i2i2−i200000000002−20
χ462-2-222-22-202020-20-2000002i−2i2i−2i02−22−2−2i2i−2i2i0000-22002−200i2−i2i2−i20000−i2i2−i2i20000000000−220
χ472-2-222-22-202020-20-2000002i−2i2i−2i0−22−222i−2i2i−2i00002-200−2200−i2i2−i2i20000−i2i2−i2i20000000000−220
χ482-2-222-22-202020-20-2000002i−2i2i−2i0−22−22−2i2i−2i2i0000-2200−2200−i2i2−i2i20000i2−i2i2−i200000000002−20
χ492-2-222-22-202020-20-200000−2i2i−2i2i02−22−22i−2i2i−2i0000-22002−200−i2i2−i2i20000i2−i2i2−i20000000000−220
χ502-2-222-22-202020-20-200000−2i2i−2i2i02−22−2−2i2i−2i2i00002-2002−200−i2i2−i2i20000−i2i2−i2i200000000002−20
χ512-2-222-22-202020-20-200000−2i2i−2i2i0−22−222i−2i2i−2i0000-2200−2200i2−i2i2−i20000−i2i2−i2i200000000002−20
χ522-2-222-22-202020-20-200000−2i2i−2i2i0−22−22−2i2i−2i2i00002-200−2200i2−i2i2−i20000i2−i2i2−i20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-44-4-4-444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ5544-44-44-4-440-40-4040000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ5644-44-44-4-440-40-404000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ5744-4-4-4-4444040-40-4004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ5844-4-4-4-4444040-40-400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ5944-4-4-4-444-40-404040000000000000000000000000000000000022−22−222200000000000000000
χ6044-4-4-4-444-40-4040400000000000000000000000000000000000−222222−2200000000000000000
χ614-444-4-4-440000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ624-444-4-4-440000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ634-444-4-4-44000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ644-444-4-4-44000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ654-4-444-44-40-40-40404000000000022−2222−22000000000000−2222000000000000000000000000000
χ664-4-444-44-40-40-404040000000000−2222−222200000000000022−22000000000000000000000000000
χ674-4-4-444-44040-40-40400000000000000000000000000000022−22−2222000000000000000000000
χ684-4-4-444-44040-40-404000000000000000000000000000000−222222−22000000000000000000000
χ694-4-4-444-440-404040-4000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-444-440-404040-400000-444-40000000000000000000000000000000000000000000000
χ718-88-8-888-8000000000000000000000000000000000000000000000000000000000000000

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