Finite Group Databasebeta

← Group #308024

Character table — Group #308024

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-11-1-111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-1-11111-1-1-1
χ911111111111111111-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-111-1-1111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111111-1-1111-1-1-1-1-1-11
χ172222222222-2-2-222-2-200002222-20000222222-2-20000000000-2-200000000-2000000000000
χ182222222222-2-2-222-2-200002222-20000-2-2-2-2-2-2-2-2000000000022000000002000000000000
χ192222222222-2-2-222-2-20000-2-2-2-2-200002222-2-2220000000000-2-2000000002000000000000
χ202222222222-2-2-222-2-20000-2-2-2-2-20000-2-2-2-2222200000000002200000000-2000000000000
χ2122222222-2-2222-2-22-222220000-222220000000022-2-20000-2-2000000000000000-20000000
χ2222222222-2-2222-2-22-222220000-2-2-2-2-200000000-2-2-2-200002200000000000000020000000
χ2322222222-2-2222-2-22-2-2-2-2-20000-2222200000000-2-2220000-2-200000000000000020000000
χ2422222222-2-2222-2-22-2-2-2-2-20000-2-2-2-2-2000000002222000022000000000000000-20000000
χ25222-2-2-22-2222-22-2-2-2222-2-20000-2000000000000002-222-2-200000000000002-20000000000
χ26222-2-2-22-2222-22-2-2-2222-2-20000-2000000000000002-2-2-2220000000000000-220000000000
χ27222-2-2-22-2222-22-2-2-22-2-2220000-200000000000000-2222-2-20000000000000-220000000000
χ28222-2-2-22-2222-22-2-2-22-2-2220000-200000000000000-22-2-22200000000000002-20000000000
χ29222-2-2-22-2-2-22-2222-2-222-2-22i2i−2i−2i200000000002i−2i00-2200000000000000000002i−2i00000000
χ30222-2-2-22-2-2-22-2222-2-222-2-2−2i−2i2i2i20000000000−2i2i00-220000000000000000000−2i2i00000000
χ31222-2-2-22-2-2-22-2222-2-2-2-2222i2i−2i−2i200000000002i−2i002-20000000000000000000−2i2i00000000
χ32222-2-2-22-2-2-22-2222-2-2-2-222−2i−2i2i2i20000000000−2i2i002-200000000000000000002i−2i00000000
χ33222-2-2-22-2-2-2-22-2222200002i2i−2i−2i-20000000000−2i2i00000000000022-2-200000000002i−2i00000
χ34222-2-2-22-2-2-2-22-2222200002i2i−2i−2i-20000000000−2i2i000000000000-2-2220000000000−2i2i00000
χ35222-2-2-22-2-2-2-22-222220000−2i−2i2i2i-200000000002i−2i00000000000022-2-20000000000−2i2i00000
χ36222-2-2-22-2-2-2-22-222220000−2i−2i2i2i-200000000002i−2i000000000000-2-22200000000002i−2i00000
χ3722-2-2-22-222-20002-20000002i−2i2i−2i0i2i2−i2−i222-2-22i−2i0000002−22−2i2−i2000000i2i2−i2−i200000000002−20
χ3822-2-2-22-222-20002-20000002i−2i2i−2i0i2i2−i2−i2-2-222−2i2i0000002−22−2i2−i2000000−i2−i2i2i20000000000−220
χ3922-2-2-22-222-20002-20000002i−2i2i−2i0−i2−i2i2i222-2-22i−2i000000−22−22−i2i2000000−i2−i2i2i20000000000−220
χ4022-2-2-22-222-20002-20000002i−2i2i−2i0−i2−i2i2i2-2-222−2i2i000000−22−22−i2i2000000i2i2−i2−i200000000002−20
χ4122-2-2-22-222-20002-2000000−2i2i−2i2i0i2i2−i2−i222-2-2−2i2i000000−22−22i2−i2000000i2i2−i2−i20000000000−220
χ4222-2-2-22-222-20002-2000000−2i2i−2i2i0i2i2−i2−i2-2-2222i−2i000000−22−22i2−i2000000−i2−i2i2i200000000002−20
χ4322-2-2-22-222-20002-2000000−2i2i−2i2i0−i2−i2i2i222-2-2−2i2i0000002−22−2−i2i2000000−i2−i2i2i200000000002−20
χ4422-2-2-22-222-20002-2000000−2i2i−2i2i0−i2−i2i2i2-2-2222i−2i0000002−22−2−i2i2000000i2i2−i2−i20000000000−220
χ452-2-22-2-2220022-200-202i−2i2i−2i000002-22-22−22−200002i−2i000000002−2i2−i2i2−i22−22−200000000i2−i2000
χ462-2-22-2-2220022-200-202i−2i2i−2i000002-22-2−22−2200002i−2i00000000−22−i2i2−i2i2−22−2200000000−i2i2000
χ472-2-22-2-2220022-200-202i−2i2i−2i00000-22-222−22−20000−2i2i000000002−2i2−i2i2−i2−22−2200000000−i2i2000
χ482-2-22-2-2220022-200-202i−2i2i−2i00000-22-22−22−220000−2i2i00000000−22−i2i2−i2i22−22−200000000i2−i2000
χ492-2-22-2-2220022-200-20−2i2i−2i2i000002-22-22−22−20000−2i2i000000002−2−i2i2−i2i22−22−200000000−i2i2000
χ502-2-22-2-2220022-200-20−2i2i−2i2i000002-22-2−22−220000−2i2i00000000−22i2−i2i2−i2−22−2200000000i2−i2000
χ512-2-22-2-2220022-200-20−2i2i−2i2i00000-22-222−22−200002i−2i000000002−2−i2i2−i2i2−22−2200000000i2−i2000
χ522-2-22-2-2220022-200-20−2i2i−2i2i00000-22-22−22−2200002i−2i00000000−22i2−i2i2−i22−22−200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-444-44-4-4-44-4000000004000000000000000000000000000000000000000000000
χ5544-444-4-4-44-4000-4400000000000000000000000000022−22−22220000000000000000000000000
χ5644-444-4-4-44-4000-44000000000000000000000000000−222222−220000000000000000000000000
χ5744-444-4-4-4-440004-40000004-4-440000000000000000000000000000000000000000000000
χ5844-444-4-4-4-440004-4000000-444-40000000000000000000000000000000000000000000000
χ5944-4-4-44-44-44000-44000000000002i22i2−2i2−2i20000000000000000−2i22i200000000000000000000000
χ6044-4-4-44-44-44000-4400000000000−2i2−2i22i22i200000000000000002i2−2i200000000000000000000000
χ614-44-44-4-440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ624-44-44-4-440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ634-44-44-4-44000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ644-44-44-4-44000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ654-4-44-4-44400-4-440040000000000000022−2222−2200000000000000−2222000000000000000000000
χ664-4-44-4-44400-4-4400400000000000000−2222−22220000000000000022−22000000000000000000000
χ674-4-4-4444-4004-4-400404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ684-4-4-4444-4004-4-40040−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-4-4444-400-44400-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ704-4-4-4444-400-44400-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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