Finite Group Databasebeta

← Group #311124

Character table — Group #311124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1111-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1111-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-111111-1-1-11
χ172222222222-2-22-2-22000000002222-2-200002222-2-2-2-20000000000-2-200-2-22200000000000000000000
χ182222222222-2-22-2-22000000002222-2-20000-2-2-2-222220000000000-2-20022-2-200000000000000000000
χ192222222222-2-22-2-2200000000-2-2-2-2-2-200002222-2-2-2-20000000000220022-2-200000000000000000000
χ202222222222-2-22-2-2200000000-2-2-2-2-2-20000-2-2-2-2222200000000002200-2-22200000000000000000000
χ2122222222-2-222-222-2222222220000-2-2-2-2-2-20000000000000000220022000000000000-200-200000000
χ2222222222-2-222-222-2222222220000-2-2-2-2-2-20000000000000000-2-200-2-2000000000000200200000000
χ2322222222-2-222-222-2-2-2-2-2-2-2-2-20000-2-2222200000000000000002200-2-2000000000000-200200000000
χ2422222222-2-222-222-2-2-2-2-2-2-2-2-20000-2-222220000000000000000-2-20022000000000000200-200000000
χ25222-2-22-2-2-2-20020022222−2−2−2−222-2-20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2000000002i−2i22−2−2i2i2−i2−i2000000000000
χ26222-2-22-2-2-2-20020022222−2−2−2−222-2-20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i200000000−2i2i22−2−2−i2−i2i2i2000000000000
χ27222-2-22-2-2-2-20020022222−2−2−2−2-2-2220022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i200000000−2i2i−2−222−i2−i2i2i2000000000000
χ28222-2-22-2-2-2-20020022222−2−2−2−2-2-2220022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2000000002i−2i−2−222i2i2−i2−i2000000000000
χ29222-2-22-2-2-2-2002002−2−2−2−2222222-2-200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2000000002i−2i−2−222−i2−i2i2i2000000000000
χ30222-2-22-2-2-2-2002002−2−2−2−2222222-2-200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i200000000−2i2i−2−222i2i2−i2−i2000000000000
χ31222-2-22-2-2-2-2002002−2−2−2−22222-2-22200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i200000000−2i2i22−2−2i2i2−i2−i2000000000000
χ32222-2-22-2-2-2-2002002−2−2−2−22222-2-22200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2000000002i−2i22−2−2−i2−i2i2i2000000000000
χ3322-22-2-22-22-2-2-2222-22i2i−2i−2i2i2i−2i−2i0000-222i−2i2i−2i000000000000000000000000000000000002-202i−2i000000
χ3422-22-2-22-22-2-2-2222-22i2i−2i−2i2i2i−2i−2i0000-222i−2i2i−2i00000000000000000000000000000000000-220−2i2i000000
χ3522-22-2-22-22-2-2-2222-2−2i−2i2i2i−2i−2i2i2i0000-22−2i2i−2i2i000000000000000000000000000000000002-20−2i2i000000
χ3622-22-2-22-22-2-2-2222-2−2i−2i2i2i−2i−2i2i2i0000-22−2i2i−2i2i00000000000000000000000000000000000-2202i−2i000000
χ3722-22-2-22-2-2222-2-2-22000000002i−2i2i−2i-2200000000000022-2-222-2-2002i−2i00000000002i−2i2i−2i000000000000
χ3822-22-2-22-2-2222-2-2-22000000002i−2i2i−2i-22000000000000-2-222-2-222002i−2i0000000000−2i2i−2i2i000000000000
χ3922-22-2-22-2-2222-2-2-2200000000−2i2i−2i2i-2200000000000022-2-222-2-200−2i2i0000000000−2i2i−2i2i000000000000
χ4022-22-2-22-2-2222-2-2-2200000000−2i2i−2i2i-22000000000000-2-222-2-22200−2i2i00000000002i−2i2i−2i000000000000
χ4122-22-2-22-2-22-2-2-22222i2i−2i−2i2i2i−2i−2i2i−2i2i−2i2-2−2i2i−2i2i000000000000000000−2i2i0000002-22-20000000000000000
χ4222-22-2-22-2-22-2-2-22222i2i−2i−2i2i2i−2i−2i−2i2i−2i2i2-2−2i2i−2i2i0000000000000000002i−2i000000-22-220000000000000000
χ4322-22-2-22-2-22-2-2-2222−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i2-22i−2i2i−2i000000000000000000−2i2i000000-22-220000000000000000
χ4422-22-2-22-2-22-2-2-2222−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i2-22i−2i2i−2i0000000000000000002i−2i0000002-22-20000000000000000
χ4522-2-22-2-222-200-2002i2i2−i2−i2−i2−i2i2i22i−2i−2i2i00−i2i2i2−i2000022-2-2i2i2−i2−i2−i2−i2i2i20000002i−2i002−2−22−222−2000000000000
χ4622-2-22-2-222-200-2002i2i2−i2−i2−i2−i2i2i22i−2i−2i2i00−i2i2i2−i20000-2-222−i2−i2i2i2i2i2−i2−i2000000−2i2i002−2−222−2−22000000000000
χ4722-2-22-2-222-200-2002i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i00−i2i2i2−i2000022-2-2i2i2−i2−i2−i2−i2i2i2000000−2i2i00−222−22−2−22000000000000
χ4822-2-22-2-222-200-2002i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i00−i2i2i2−i20000-2-222−i2−i2i2i2i2i2−i2−i20000002i−2i00−222−2−222−2000000000000
χ4922-2-22-2-222-200-2002−i2−i2i2i2i2i2−i2−i22i−2i−2i2i00i2−i2−i2i2000022-2-2−i2−i2i2i2i2i2−i2−i20000002i−2i00−222−22−2−22000000000000
χ5022-2-22-2-222-200-2002−i2−i2i2i2i2i2−i2−i22i−2i−2i2i00i2−i2−i2i20000-2-222i2i2−i2−i2−i2−i2i2i2000000−2i2i00−222−2−222−2000000000000
χ5122-2-22-2-222-200-2002−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i00i2−i2−i2i2000022-2-2−i2−i2i2i2i2i2−i2−i2000000−2i2i002−2−22−222−2000000000000
χ5222-2-22-2-222-200-2002−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i00i2−i2−i2i20000-2-222i2i2−i2−i2−i2−i2i2i20000002i−2i002−2−222−2−22000000000000
χ532-22-22-22-2002-202-202i−2i2i−2i2i−2i2i−2i0000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−22i−2i002-20000000000000000002−2i2−i200
χ542-22-22-22-2002-202-202i−2i2i−2i2i−2i2i−2i0000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2−2i2i00-22000000000000000000−22−i2i200
χ552-22-22-22-2002-202-202i−2i2i−2i2i−2i2i−2i0000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−222i−2i002-2000000000000000000−22−i2i200
χ562-22-22-22-2002-202-202i−2i2i−2i2i−2i2i−2i0000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22−2i2i00-220000000000000000002−2i2−i200
χ572-22-22-22-2002-202-20−2i2i−2i2i−2i2i−2i2i0000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−222i−2i00-220000000000000000002−2−i2i200
χ582-22-22-22-2002-202-20−2i2i−2i2i−2i2i−2i2i0000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22−2i2i002-2000000000000000000−22i2−i200
χ592-22-22-22-2002-202-20−2i2i−2i2i−2i2i−2i2i0000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−22i−2i00-22000000000000000000−22i2−i200
χ602-22-22-22-2002-202-20−2i2i−2i2i−2i2i−2i2i0000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2−2i2i002-20000000000000000002−2−i2i200
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-4-44-4-44400-400-422222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ63444-4-44-4-44400-400-4−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-44-4-44-44-4444-4-4-40000000000004-400000000000000000000000000000000000000000000000000
χ6544-4-44-4-44-4400400-42i22i2−2i2−2i2−2i2−2i22i22i20000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ6644-4-44-4-44-4400400-4−2i2−2i22i22i22i22i2−2i2−2i2000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ674-444-4-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000022−22−22220000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ684-444-4-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000−222222−2200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ694-444-4-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000022−22−222200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ704-444-4-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000−222222−220000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ714-44-44-44-400-440-4400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ724-44-44-44-400-440-440000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ734-4-4444-4-40000000022−22−2222−222222−22000000000000002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ744-4-4444-4-40000000022−22−2222−222222−2200000000000000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ754-4-4444-4-400000000−222222−2222−22−2222000000000000002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ764-4-4444-4-400000000−222222−2222−22−222200000000000000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ774-4-4-4-4444004-40-4400000000000000000000000000022−22−222222−22−2222000000000000000000000000000000
χ784-4-4-4-4444004-40-44000000000000000000000000000−222222−22−222222−22000000000000000000000000000000
χ794-4-4-4-444400-4404-404-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ804-4-4-4-444400-4404-40-444-4-444-400000000000000000000000000000000000000000000000000000000

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