Finite Group Databasebeta

← Group #306368

Character table — Group #306368

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-11111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-111-1-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-11111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111111111-1-11-1-1-1-1-1-11
χ17222222222-22-22-22-2-200002222-22222000000-2-22200000000-2-20000000000000-20000000
χ18222222222-22-22-22-2-200002222-2-2-2-2-2000000-2-2-2-20000000022000000000000020000000
χ19222222222-22-22-22-2-20000-2-2-2-2-2222200000022-2-200000000-2-2000000000000020000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2-2-2000000222200000000220000000000000-20000000
χ2122222222-22-22-22-22-222220000-200002222220000-2-2-2-200000000000000-2000000000000
χ2222222222-22-22-22-22-222220000-20000-2-2-2-2-2-20000-2-222000000000000002000000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-200002222-2-2000022-2-2000000000000002000000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-20000-2-2-2-2220000222200000000000000-2000000000000
χ25222-2-2-22-22-2-222-2-22-222-2-200002000000000000002-2002i2i−2i−2i00000000000000002i−2i00000
χ26222-2-2-22-22-2-222-2-22-222-2-200002000000000000002-200−2i−2i2i2i0000000000000000−2i2i00000
χ27222-2-2-22-22-2-222-2-22-2-2-2220000200000000000000-22002i2i−2i−2i0000000000000000−2i2i00000
χ28222-2-2-22-22-2-222-2-22-2-2-2220000200000000000000-2200−2i−2i2i2i00000000000000002i−2i00000
χ29222-2-2-22-2-222-2-222-2-200002i2i−2i−2i200000000002i−2i00000000000022-2-200000002i−2i00000000
χ30222-2-2-22-2-222-2-222-2-200002i2i−2i−2i200000000002i−2i000000000000-2-2220000000−2i2i00000000
χ31222-2-2-22-2-222-2-222-2-20000−2i−2i2i2i20000000000−2i2i00000000000022-2-20000000−2i2i00000000
χ32222-2-2-22-2-222-2-222-2-20000−2i−2i2i2i20000000000−2i2i000000000000-2-22200000002i−2i00000000
χ33222-2-2-22-2-2-222-2-222222-2-22i2i−2i−2i-20000000000−2i2i00-22000000000000000002i−2i0000000000
χ34222-2-2-22-2-2-222-2-222222-2-2−2i−2i2i2i-200000000002i−2i00-2200000000000000000−2i2i0000000000
χ35222-2-2-22-2-2-222-2-2222-2-2222i2i−2i−2i-20000000000−2i2i002-200000000000000000−2i2i0000000000
χ36222-2-2-22-2-2-222-2-2222-2-222−2i−2i2i2i-200000000002i−2i002-2000000000000000002i−2i0000000000
χ3722-22-2-2-2220-20-2020000002-22-202i2i−2i−2ii2i2−i2−i200002i−2i00i2−i2i2−i2i2−i200000022−2−200000000002−20
χ3822-22-2-2-2220-20-2020000002-22-202i2i−2i−2i−i2−i2i2i200002i−2i00−i2i2−i2i2−i2i2000000−2−2220000000000−220
χ3922-22-2-2-2220-20-2020000002-22-20−2i−2i2i2ii2i2−i2−i20000−2i2i00i2−i2i2−i2i2−i2000000−2−2220000000000−220
χ4022-22-2-2-2220-20-2020000002-22-20−2i−2i2i2i−i2−i2i2i20000−2i2i00−i2i2−i2i2−i2i200000022−2−200000000002−20
χ4122-22-2-2-2220-20-202000000-22-2202i2i−2i−2ii2i2−i2−i20000−2i2i00i2−i2−i2i2−i2i200000022−2−20000000000−220
χ4222-22-2-2-2220-20-202000000-22-2202i2i−2i−2i−i2−i2i2i20000−2i2i00−i2i2i2−i2i2−i2000000−2−22200000000002−20
χ4322-22-2-2-2220-20-202000000-22-220−2i−2i2i2ii2i2−i2−i200002i−2i00i2−i2−i2i2−i2i2000000−2−22200000000002−20
χ4422-22-2-2-2220-20-202000000-22-220−2i−2i2i2i−i2−i2i2i200002i−2i00−i2i2i2−i2i2−i200000022−2−20000000000−220
χ452-2-2-22-22202020-20-202i−2i2i−2i000002−22−22i−2i2i−2i2-20000000000002−2i2−i2i2−i2i2−i2i2−i2000000002−2000
χ462-2-2-22-22202020-20-202i−2i2i−2i000002−22−2−2i2i−2i2i-220000000000002−2i2−i2i2−i2−i2i2−i2i200000000−22000
χ472-2-2-22-22202020-20-202i−2i2i−2i00000−22−222i−2i2i−2i2-2000000000000−22−i2i2−i2i2−i2i2−i2i200000000−22000
χ482-2-2-22-22202020-20-202i−2i2i−2i00000−22−22−2i2i−2i2i-22000000000000−22−i2i2−i2i2i2−i2i2−i2000000002−2000
χ492-2-2-22-22202020-20-20−2i2i−2i2i000002−22−22i−2i2i−2i-220000000000002−2−i2i2−i2i2i2−i2i2−i200000000−22000
χ502-2-2-22-22202020-20-20−2i2i−2i2i000002−22−2−2i2i−2i2i2-20000000000002−2−i2i2−i2i2−i2i2−i2i2000000002−2000
χ512-2-2-22-22202020-20-20−2i2i−2i2i00000−22−222i−2i2i−2i-22000000000000−22i2−i2i2−i2−i2i2−i2i2000000002−2000
χ522-2-2-22-22202020-20-20−2i2i−2i2i00000−22−22−2i2i−2i2i2-2000000000000−22i2−i2i2−i2i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ5544-44-4-4-44-404040-40000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ5644-44-4-4-44-404040-4000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ5744-4-444-4-44040-40-40000000000000000000000000000022−22−222200000000000000000000000
χ5844-4-444-4-44040-40-400000000000000000000000000000−222222−2200000000000000000000000
χ5944-4-444-4-4-40-404040000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6044-4-444-4-4-40-40404000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ614-44-4-44-440000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ624-44-4-44-440000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ634-44-4-44-44000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ644-44-4-44-44000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ654-4-44-444-4040-40-40400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ664-4-44-444-4040-40-4040000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ674-4-44-444-40-404040-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ684-4-44-444-40-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-4-44-4440-40-40404000000000022−2222−22000000000000000000−2222000000000000000000000
χ704-4-4-44-4440-40-404040000000000−2222−222200000000000000000022−22000000000000000000000
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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