Finite Group Databasebeta

← Group #269821

Character table — Group #269821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888882222444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-11111-1-1-1-111111111-11-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-11111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11-1-1-111111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111111111-1-111-1-1-1-1-1-11
χ17222222222-2-2222-2-20000-22222-200002222-2-2000022-2-200000000000000-2000000000000
χ18222222222-2-2222-2-20000-22222-20000-2-2-2-2-2-20000-2-222000000000000002000000000000
χ19222222222-2-2222-2-20000-2-2-2-2-2-200002222220000-2-2-2-2000000000000002000000000000
χ20222222222-2-2222-2-20000-2-2-2-2-2-20000-2-2-2-2220000222200000000000000-2000000000000
χ2122222222-222-2-2-2222222-20000-2222200000022-2-20000-2-20000000000000-200000000000
χ2222222222-222-2-2-2222222-20000-2-2-2-2-2000000-2-2-2-20000220000000000000200000000000
χ2322222222-222-2-2-222-2-2-2-2-20000-22222000000-2-2220000-2-20000000000000200000000000
χ2422222222-222-2-2-222-2-2-2-2-20000-2-2-2-2-200000022220000220000000000000-200000000000
χ25222-2-2-2-2202-20002-222-2-200000022-2-2i2i2−i2−i2002-20000i2−i2000000i2i2−i2−i2i2i2−i2−i200000000i2−i2000
χ26222-2-2-2-2202-20002-222-2-200000022-2-2−i2−i2i2i2002-20000−i2i2000000−i2−i2i2i2−i2−i2i2i200000000−i2i2000
χ27222-2-2-2-2202-20002-222-2-2000000-2-222i2i2−i2−i200-220000i2−i2000000i2i2−i2−i2−i2−i2i2i200000000−i2i2000
χ28222-2-2-2-2202-20002-222-2-2000000-2-222−i2−i2i2i200-220000−i2i2000000−i2−i2i2i2i2i2−i2−i200000000i2−i2000
χ29222-2-2-2-2202-20002-2-2-22200000022-2-2i2i2−i2−i200-220000i2−i2000000−i2−i2i2i2i2i2−i2−i200000000−i2i2000
χ30222-2-2-2-2202-20002-2-2-22200000022-2-2−i2−i2i2i200-220000−i2i2000000i2i2−i2−i2−i2−i2i2i200000000i2−i2000
χ31222-2-2-2-2202-20002-2-2-222000000-2-222i2i2−i2−i2002-20000i2−i2000000−i2−i2i2i2−i2−i2i2i200000000i2−i2000
χ32222-2-2-2-2202-20002-2-2-222000000-2-222−i2−i2i2i2002-20000−i2i2000000i2i2−i2−i2i2i2−i2−i200000000−i2i2000
χ3322-222-2-2-2-200-22200000002i2i−2i−2i02−22−22-22-20000002i−2i002−2i2i2−i2−i200002−22−20000000000i2−i20
χ3422-222-2-2-2-200-22200000002i2i−2i−2i02−22−2-22-22000000−2i2i002−2i2i2−i2−i20000−22−220000000000−i2i20
χ3522-222-2-2-2-200-22200000002i2i−2i−2i0−22−222-22-20000002i−2i00−22−i2−i2i2i20000−22−220000000000−i2i20
χ3622-222-2-2-2-200-22200000002i2i−2i−2i0−22−22-22-22000000−2i2i00−22−i2−i2i2i200002−22−20000000000i2−i20
χ3722-222-2-2-2-200-2220000000−2i−2i2i2i02−22−22-22-2000000−2i2i002−2−i2−i2i2i200002−22−20000000000−i2i20
χ3822-222-2-2-2-200-2220000000−2i−2i2i2i02−22−2-22-220000002i−2i002−2−i2−i2i2i20000−22−220000000000i2−i20
χ3922-222-2-2-2-200-2220000000−2i−2i2i2i0−22−222-22-2000000−2i2i00−22i2i2−i2−i20000−22−220000000000i2−i20
χ4022-222-2-2-2-200-2220000000−2i−2i2i2i0−22−22-22-220000002i−2i00−22i2i2−i2−i200002−22−20000000000−i2i20
χ412-2-2-222-22222-22-2-2-2000022-22-2-2000000002-2000000000000002i−2i2i−2i0000002i−2i000000000
χ422-2-2-222-22222-22-2-2-2000022-22-2-2000000002-200000000000000−2i2i−2i2i000000−2i2i000000000
χ432-2-2-222-22222-22-2-2-200002-22-22-200000000-22000000000000002i−2i2i−2i000000−2i2i000000000
χ442-2-2-222-22222-22-2-2-200002-22-22-200000000-2200000000000000−2i2i−2i2i0000002i−2i000000000
χ452-2-2-222-222-2-2-22-2222-22-2-22-22-2200000000-22002-200000000000000000000002-20000000
χ462-2-2-222-222-2-2-22-2222-22-2-2-22-222000000002-2002-20000000000000000000000-220000000
χ472-2-2-222-222-2-2-22-222-22-22-22-22-2200000000-2200-220000000000000000000000-220000000
χ482-2-2-222-222-2-2-22-222-22-22-2-22-222000000002-200-2200000000000000000000002-20000000
χ492-2-2-222-22-2-2-22-22222-22-220000-2000000000000-220000002-22-2000000000000002-200000
χ502-2-2-222-22-2-2-22-22222-22-220000-2000000000000-22000000-22-2200000000000000-2200000
χ512-2-2-222-22-2-2-22-2222-22-2220000-20000000000002-20000002-22-200000000000000-2200000
χ522-2-2-222-22-2-2-22-2222-22-2220000-20000000000002-2000000-22-22000000000000002-200000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-440-44000-44000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ55444-4-4-4-440-44000-4400000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ5644-444-4-4-44004-4-400000000000022−2222−2200000000000000−22220000000000000000000000000
χ5744-444-4-4-44004-4-4000000000000−2222−22220000000000000022−220000000000000000000000000
χ5844-4-4-444-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ5944-4-4-444-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ6044-4-4-444-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ6144-4-4-444-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ624-44-44-44-4400-4-44000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ634-44-44-44-4400-4-4400000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ644-44-44-44-4-40044-400000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ654-44-44-44-4-40044-40000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ664-4-44-4-44404-4000-44000000000000000000000000000000000022−22−222200000000000000000
χ674-4-44-4-44404-4000-440000000000000000000000000000000000−222222−2200000000000000000
χ684-4-44-4-4440-440004-44-4-44000000000000000000000000000000000000000000000000000
χ694-4-44-4-4440-440004-4-444-4000000000000000000000000000000000000000000000000000
χ704-4-4-444-44-4444-44-4-40000-400004000000000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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