Finite Group Databasebeta

← Group #310214

Character table — Group #310214

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-111-1-11111-1-1-1-111111111-1-1-11-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-11111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-22-2-222-20000-22222-2000022222200-2-20000-2-2000000000000000-2000000000
χ18222222222-22-2-222-20000-22222-20000-2-2-2-2-2-200-2-20000220000000000000002000000000
χ19222222222-22-2-222-20000-2-2-2-2-2-200002222-2-200220000-2-20000000000000002000000000
χ20222222222-22-2-222-20000-2-2-2-2-2-20000-2-2-2-2220022000022000000000000000-2000000000
χ2122222222-22-222-2-222222-20000-22222000000-2-20022-2-200000000000000-2000000000000
χ2222222222-22-222-2-222222-20000-2-2-2-2-2000000-2-200-2-222000000000000002000000000000
χ2322222222-22-222-2-22-2-2-2-2-20000-222220000002200-2-2-2-2000000000000002000000000000
χ2422222222-22-222-2-22-2-2-2-2-20000-2-2-2-2-20000002200222200000000000000-2000000000000
χ25222-2-2-2-220-202-200222-2-20000002i2i−2i−2i22−2−20000002i−2i002−222−2−20000i2i2−i2−i200000000i2−i2000
χ26222-2-2-2-220-202-200222-2-20000002i2i−2i−2i−2−2220000002i−2i00−22−2−2220000−i2−i2i2i200000000−i2i2000
χ27222-2-2-2-220-202-200222-2-2000000−2i−2i2i2i22−2−2000000−2i2i002−222−2−20000−i2−i2i2i200000000−i2i2000
χ28222-2-2-2-220-202-200222-2-2000000−2i−2i2i2i−2−222000000−2i2i00−22−2−2220000i2i2−i2−i200000000i2−i2000
χ29222-2-2-2-220-202-2002-2-2220000002i2i−2i−2i22−2−2000000−2i2i002−2−2−2220000i2i2−i2−i200000000−i2i2000
χ30222-2-2-2-220-202-2002-2-2220000002i2i−2i−2i−2−222000000−2i2i00−2222−2−20000−i2−i2i2i200000000i2−i2000
χ31222-2-2-2-220-202-2002-2-222000000−2i−2i2i2i22−2−20000002i−2i002−2−2−2220000−i2−i2i2i200000000i2−i2000
χ32222-2-2-2-220-202-2002-2-222000000−2i−2i2i2i−2−2220000002i−2i00−2222−2−20000i2i2−i2−i200000000−i2i2000
χ3322-2-2-222-220-200-220000002i2i−2i−2i0i2−i2i2−i22-22-22i−2i000000i2−i200000022−2−2i2−i2i2−i200000000002−20
χ3422-2-2-222-220-200-220000002i2i−2i−2i0i2−i2i2−i2-22-22−2i2i000000i2−i200000022−2−2−i2i2−i2i20000000000−220
χ3522-2-2-222-220-200-220000002i2i−2i−2i0−i2i2−i2i22-22-22i−2i000000−i2i2000000−2−222−i2i2−i2i20000000000−220
χ3622-2-2-222-220-200-220000002i2i−2i−2i0−i2i2−i2i2-22-22−2i2i000000−i2i2000000−2−222i2−i2i2−i200000000002−20
χ3722-2-2-222-220-200-22000000−2i−2i2i2i0i2−i2i2−i22-22-2−2i2i000000i2−i2000000−2−222i2−i2i2−i20000000000−220
χ3822-2-2-222-220-200-22000000−2i−2i2i2i0i2−i2i2−i2-22-222i−2i000000i2−i2000000−2−222−i2i2−i2i200000000002−20
χ3922-2-2-222-220-200-22000000−2i−2i2i2i0−i2i2−i2i22-22-2−2i2i000000−i2i200000022−2−2−i2i2−i2i200000000002−20
χ4022-2-2-222-220-200-22000000−2i−2i2i2i0−i2i2−i2i2-22-222i−2i000000−i2i200000022−2−2i2−i2i2−i20000000000−220
χ412-2-22-22-2222-2-2-22-22000022i−2i2i−2i-20000000000002i−2i0000002-22-20000000000002i−2i0000000
χ422-2-22-22-2222-2-2-22-22000022i−2i2i−2i-20000000000002i−2i000000-22-22000000000000−2i2i0000000
χ432-2-22-22-2222-2-2-22-2200002−2i2i−2i2i-2000000000000−2i2i0000002-22-2000000000000−2i2i0000000
χ442-2-22-22-2222-2-2-22-2200002−2i2i−2i2i-2000000000000−2i2i000000-22-220000000000002i−2i0000000
χ452-2-22-22-222-2-2222-2-22i−2i2i−2i-22i−2i2i−2i200000000002i−2i−2i2i00000000000000000002-20000000000
χ462-2-22-22-222-2-2222-2-22i−2i2i−2i-2−2i2i−2i2i200000000002i−2i2i−2i0000000000000000000-220000000000
χ472-2-22-22-222-2-2222-2-2−2i2i−2i2i-22i−2i2i−2i20000000000−2i2i−2i2i0000000000000000000-220000000000
χ482-2-22-22-222-2-2222-2-2−2i2i−2i2i-2−2i2i−2i2i20000000000−2i2i2i−2i00000000000000000002-20000000000
χ492-2-22-22-22-2-2222-22-22i−2i2i−2i20000-20000000000−2i2i0000000000002i−2i2i−2i00000000002-200000
χ502-2-22-22-22-2-2222-22-22i−2i2i−2i20000-20000000000−2i2i000000000000−2i2i−2i2i0000000000-2200000
χ512-2-22-22-22-2-2222-22-2−2i2i−2i2i20000-200000000002i−2i0000000000002i−2i2i−2i0000000000-2200000
χ522-2-22-22-22-2-2222-22-2−2i2i−2i2i20000-200000000002i−2i000000000000−2i2i−2i2i00000000002-200000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-44040-4400-4000000000000002222−22−220000000000−22220000000000000000000000000
χ55444-4-4-4-44040-4400-400000000000000−22−222222000000000022−220000000000000000000000000
χ5644-444-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ5744-444-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ5844-444-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ5944-444-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ6044-4-4-444-4-404004-4000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ6144-4-4-444-4-404004-400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ624-44-444-4-440400-4-40000004-4-440000000000000000000000000000000000000000000000
χ634-44-444-4-440400-4-4000000-444-40000000000000000000000000000000000000000000000
χ644-44-444-4-4-40-40044000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ654-44-444-4-4-40-4004400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ664-4-44-44-44-444-4-4-4440000-400004000000000000000000000000000000000000000000000
χ674-4-4-44-4440404-400-44i−4i−4i4i000000000000000000000000000000000000000000000000000
χ684-4-4-44-4440404-400-4−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ694-4-4-44-4440-40-4400400000000000000000000000000000022−22−2222000000000000000000000
χ704-4-4-44-4440-40-44004000000000000000000000000000000−222222−22000000000000000000000
χ718-888-8-88-8000000000000000000000000000000000000000000000000000000000000000

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