Finite Group Databasebeta

← Group #308021

Character table — Group #308021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-111-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111111-1-1-1-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11111-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111111111-1-1-1-1111-1-1-1-11
χ17222222222-2-22-222-22222-20000-222220000220000-2-2000000-2-2000000000000000-200000
χ18222222222-2-22-222-22222-20000-2-2-2-2-20000-2-20000-2-200000022000000000000000200000
χ19222222222-2-22-222-2-2-2-2-2-20000-222220000-2-2000022000000-2-2000000000000000200000
χ20222222222-2-22-222-2-2-2-2-2-20000-2-2-2-2-200002200002200000022000000000000000-200000
χ2122222222-222-22-2-220000-22222-20000222200-2-22200-2-200000000000000-2000000000000
χ2222222222-222-22-2-220000-22222-20000-2-2-2-200-2-2-2-20022000000000000002000000000000
χ2322222222-222-22-2-220000-2-2-2-2-2-2000022220022-2-200-2-2000000000000002000000000000
χ2422222222-222-22-2-220000-2-2-2-2-2-20000-2-2-2-2002222002200000000000000-2000000000000
χ25222-2-2-22-2222-2-22-2-222-2-220000-2000000000000002-20022-2-200000000000002-200000000
χ26222-2-2-22-2222-2-22-2-222-2-220000-2000000000000002-200-2-2220000000000000-2200000000
χ27222-2-2-22-2222-2-22-2-2-2-22220000-200000000000000-220022-2-20000000000000-2200000000
χ28222-2-2-22-2222-2-22-2-2-2-22220000-200000000000000-2200-2-22200000000000002-200000000
χ29222-2-2-22-22-2-2-222-2222-2-2-22i2i−2i−2i200000000002i−2i00-220000000000000000000002i−2i000000
χ30222-2-2-22-22-2-2-222-2222-2-2-2−2i−2i2i2i20000000000−2i2i00-22000000000000000000000−2i2i000000
χ31222-2-2-22-22-2-2-222-22-2-222-22i2i−2i−2i200000000002i−2i002-2000000000000000000000−2i2i000000
χ32222-2-2-22-22-2-2-222-22-2-222-2−2i−2i2i2i20000000000−2i2i002-20000000000000000000002i−2i000000
χ33222-2-2-22-2-2-2-222-222000022i2i−2i−2i-20000000000−2i2i00000000000022-2-2000002i−2i0000000000
χ34222-2-2-22-2-2-2-222-222000022i2i−2i−2i-20000000000−2i2i000000000000-2-22200000−2i2i0000000000
χ35222-2-2-22-2-2-2-222-22200002−2i−2i2i2i-200000000002i−2i00000000000022-2-200000−2i2i0000000000
χ36222-2-2-22-2-2-2-222-22200002−2i−2i2i2i-200000000002i−2i000000000000-2-222000002i−2i0000000000
χ3722-2-22-2-22200-20-2202-22-20000002i2i−2i−2ii2i2−i2−i22i−2i000000i2−i2000000i2−i2i2−i222−2−200000000002−20
χ3822-2-22-2-22200-20-2202-22-20000002i2i−2i−2i−i2−i2i2i22i−2i000000−i2i2000000−i2i2−i2i2−2−2220000000000−220
χ3922-2-22-2-22200-20-2202-22-2000000−2i−2i2i2ii2i2−i2−i2−2i2i000000i2−i2000000i2−i2i2−i2−2−2220000000000−220
χ4022-2-22-2-22200-20-2202-22-2000000−2i−2i2i2i−i2−i2i2i2−2i2i000000−i2i2000000−i2i2−i2i222−2−200000000002−20
χ4122-2-22-2-22200-20-220-22-220000002i2i−2i−2ii2i2−i2−i2−2i2i000000i2−i2000000−i2i2−i2i222−2−20000000000−220
χ4222-2-22-2-22200-20-220-22-220000002i2i−2i−2i−i2−i2i2i2−2i2i000000−i2i2000000i2−i2i2−i2−2−22200000000002−20
χ4322-2-22-2-22200-20-220-22-22000000−2i−2i2i2ii2i2−i2−i22i−2i000000i2−i2000000−i2i2−i2i2−2−22200000000002−20
χ4422-2-22-2-22200-20-220-22-22000000−2i−2i2i2i−i2−i2i2i22i−2i000000−i2i2000000i2−i2i2−i222−2−20000000000−220
χ452-2-22-2-22202-20200-2000002-22-202−22−22i−2i2i−2i00002i−2i00002−22−22−20000i2−i2i2−i200000000i2−i2000
χ462-2-22-2-22202-20200-2000002-22-202−22−2−2i2i−2i2i0000−2i2i00002−22−22−20000−i2i2−i2i200000000−i2i2000
χ472-2-22-2-22202-20200-2000002-22-20−22−222i−2i2i−2i00002i−2i0000−22−22−220000−i2i2−i2i200000000−i2i2000
χ482-2-22-2-22202-20200-2000002-22-20−22−22−2i2i−2i2i0000−2i2i0000−22−22−220000i2−i2i2−i200000000i2−i2000
χ492-2-22-2-22202-20200-200000-22-2202−22−22i−2i2i−2i0000−2i2i0000−22−222−20000i2−i2i2−i200000000−i2i2000
χ502-2-22-2-22202-20200-200000-22-2202−22−2−2i2i−2i2i00002i−2i0000−22−222−20000−i2i2−i2i200000000i2−i2000
χ512-2-22-2-22202-20200-200000-22-220−22−222i−2i2i−2i0000−2i2i00002−22−2−220000−i2i2−i2i200000000i2−i2000
χ522-2-22-2-22202-20200-200000-22-220−22−22−2i2i−2i2i00002i−2i00002−22−2−220000i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4444-4-44-40000-400004000000000000000000000000000000000000000000000
χ5544-44-44-4-440040-4-404-4-44000000000000000000000000000000000000000000000000000
χ5644-44-44-4-440040-4-40-444-4000000000000000000000000000000000000000000000000000
χ5744-44-44-4-4-400-4044000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5844-44-44-4-4-400-404400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5944-4-44-4-44-400404-40000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ6044-4-44-4-44-400404-4000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
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
χ654-4-44-4-4440-440-4004000000000022−2222−22000000000000000000−2222000000000000000000000
χ664-4-44-4-4440-440-40040000000000−2222−222200000000000000000022−22000000000000000000000
χ674-4-4-4444-404-40-4004000000000000000000000000000022−22−222200000000000000000000000
χ684-4-4-4444-404-40-40040000000000000000000000000000−222222−2200000000000000000000000
χ694-4-4-4444-40-440400-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ704-4-4-4444-40-440400-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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