Finite Group Databasebeta

← Group #72315059

Character table — Group #72315059

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11222222244444488888888888161616161616161616161616161616161616161616161616161616163232323232323232323232323232323232326464646464646464646464646464
order12222222222222222222224444222222224444444444444444444444444444444444444444444444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111111-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ411111111111111111111111111111111-1-1111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-1
χ71111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ911111111111111111111111111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111111111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ1111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ1211111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-111
χ1311111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ1411111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ1511111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-111-1-11111-1-1-1-1
χ1611111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111
χ1722222222222222222-22-2-2-2-2-2-2-2002-20022002-20022000022-2-20000-2-20000000000000000002-20000000000
χ1822222222222222222-22-2-2-2-2-2-2-2002-200-2-2002-200-2-2000022-2-2000022000000000000000000-220000000000
χ1922222222222222222-22-2-2-2-2-2-2-200-22002200-2200220000-2-2220000-2-2000000000000000000-220000000000
χ2022222222222222222-22-2-2-2-2-2-2-200-2200-2-200-2200-2-20000-2-2220000220000000000000000002-20000000000
χ212222222222-2-22-2-22-2-2-2-2-2-222222200000022000000-2-2-2-200000000000000000000002i2i−2i−2i00000000002i−2i00
χ222222222222-2-22-2-22-2-2-2-2-2-222222200000022000000-2-2-2-20000000000000000000000−2i−2i2i2i0000000000−2i2i00
χ232222222222-2-22-2-22-2-2-2-2-2-22222-2-2000000-2-2000000222200000000000000000000002i2i−2i−2i0000000000−2i2i00
χ242222222222-2-22-2-22-2-2-2-2-2-22222-2-2000000-2-200000022220000000000000000000000−2i−2i2i2i00000000002i−2i00
χ25222222222-222-222-2-22-22-2-22-2-22002-20000002-200000000-2-22200000022-2-2000022-2-2000000000000000000
χ26222222222-222-222-2-22-22-2-22-2-22002-20000002-200000000-2-222000000-2-2220000-2-222000000000000000000
χ27222222222-222-222-2-22-22-2-22-2-2200-22000000-220000000022-2-200000022-2-20000-2-222000000000000000000
χ28222222222-222-222-2-22-22-2-22-2-2200-22000000-220000000022-2-2000000-2-222000022-2-2000000000000000000
χ29222222222-222-222-2-2-2-2-222-222-200220000002200000000-2-2-2-20000000000000000002-22-22-2000000000000
χ30222222222-222-222-2-2-2-2-222-222-200220000002200000000-2-2-2-2000000000000000000-22-22-22000000000000
χ31222222222-222-222-2-2-2-2-222-222-200-2-2000000-2-20000000022220000000000000000002-22-2-22000000000000
χ32222222222-222-222-2-2-2-2-222-222-200-2-2000000-2-2000000002222000000000000000000-22-222-2000000000000
χ33222222222-2-2-2-2-2-2-22222-2-2-222-2000022000000220000000000-2-2-2-2000000000000002i−2i−2i2i000000002i−2i0000
χ34222222222-2-2-2-2-2-2-22222-2-2-222-2000022000000220000000000-2-2-2-200000000000000−2i2i2i−2i00000000−2i2i0000
χ35222222222-2-2-2-2-2-2-22222-2-2-222-20000-2-2000000-2-200000000002222000000000000002i−2i−2i2i00000000−2i2i0000
χ36222222222-2-2-2-2-2-2-22222-2-2-222-20000-2-2000000-2-20000000000222200000000000000−2i2i2i−2i000000002i−2i0000
χ37222-2-22-2-222222-2-2-222-2-22-222-2-222000000-2-200000022-2-20000000000000000002i−2i2i−2i00000000002i−2i000000
χ38222-2-22-2-222222-2-2-222-2-22-222-2-222000000-2-200000022-2-2000000000000000000−2i2i−2i2i0000000000−2i2i000000
χ39222-2-22-2-222222-2-2-222-2-22-222-2-2-2-200000022000000-2-2220000000000000000002i−2i2i−2i0000000000−2i2i000000
χ40222-2-22-2-222222-2-2-222-2-22-222-2-2-2-200000022000000-2-222000000000000000000−2i2i−2i2i00000000002i−2i000000
χ41222-2-22-2-222-2-2222-2-222-22-2-2-22200002-22200002-2-2-20000000022-2-22-2000000000000000000002-200000000
χ42222-2-22-2-222-2-2222-2-222-22-2-2-22200002-2-2-200002-2220000000022-2-2-2200000000000000000000-2200000000
χ43222-2-22-2-222-2-2222-2-222-22-2-2-2220000-22220000-22-2-200000000-2-2222-200000000000000000000-2200000000
χ44222-2-22-2-222-2-2222-2-222-22-2-2-2220000-22-2-20000-222200000000-2-222-22000000000000000000002-200000000
χ45222-2-22-2-222-2-2222-2-2-222-2222-2-222000022-2-20000-2-2-2-22200000000-22000022-2-20000000000000000000000
χ46222-2-22-2-222-2-2222-2-2-222-2222-2-2220000-2-2-2-2000022-2-222000000002-20000-2-2220000000000000000000000
χ47222-2-22-2-222-2-2222-2-2-222-2222-2-2-2-2000022220000-2-222-2-200000000-220000-2-2220000000000000000000000
χ48222-2-22-2-222-2-2222-2-2-222-2222-2-2-2-20000-2-22200002222-2-2000000002-2000022-2-20000000000000000000000
χ49222-2-22-2-22-222-2-2-22-222-2-222-22-200002-20000002-20000000000-2-22200000000002i−2i−2i2i00000000000000002i−2i
χ50222-2-22-2-22-222-2-2-22-222-2-222-22-200002-20000002-20000000000-2-2220000000000−2i2i2i−2i0000000000000000−2i2i
χ51222-2-22-2-22-222-2-2-22-222-2-222-22-20000-22000000-22000000000022-2-200000000002i−2i−2i2i0000000000000000−2i2i
χ52222-2-22-2-22-222-2-2-22-222-2-222-22-20000-22000000-22000000000022-2-20000000000−2i2i2i−2i00000000000000002i−2i
χ534444444444-4-44-4-44-44-4444-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ54444444444-4-4-4-4-4-4-44-44-4444-4-44000000000000000000000000000000000000000000000000000000000000
χ55444-4-44-4-444444-4-4-44-4-44-44-4-444000000000000000000000000000000000000000000000000000000000000
χ56444-4-44-4-44-444-4-4-44-4-4444-4-44-44000000000000000000000000000000000000000000000000000000000000
χ57444-4-44-4-44-4-4-4-444444-4-4-44-44-44000000000000000000000000000000000000000000000000000000000000
χ58444-4-44-4-44-4-4-4-44444-4-444-44-44-4000000000000000000000000000000000000000000000000000000000000
χ5944-44-4-44-4404-404-4000000000002-20022002-200-2-2002-22-2004-42-22-200000000000000000000000000000000
χ6044-44-4-44-4404-404-4000000000002-200-2-2002-20022002-22-200-44-22-2200000000000000000000000000000000
χ6144-44-4-44-4404-404-400000000000-22002200-2200-2-200-22-2200-442-22-200000000000000000000000000000000
χ6244-44-4-44-4404-404-400000000000-2200-2-200-22002200-22-22004-4-22-2200000000000000000000000000000000
χ6344-44-4-44-440-440-44000000000002-20022002-200-2-200-22-224-400-22-2200000000000000000000000000000000
χ6444-44-4-44-440-440-44000000000002-200-2-2002-2002200-22-22-44002-22-200000000000000000000000000000000
χ6544-44-4-44-440-440-4400000000000-22002200-2200-2-2002-22-2-4400-22-2200000000000000000000000000000000
χ6644-44-4-44-440-440-4400000000000-2200-2-200-220022002-22-24-4002-22-200000000000000000000000000000000
χ6744-4-44-4-44404-40-44000000000002-2402-200-22-40-22002-2-220000-222-200000000000000000000000000000000
χ6844-4-44-4-44404-40-44000000000002-2-40-2200-22402-2002-2-2200002-2-2200000000000000000000000000000000
χ6944-4-44-4-44404-40-4400000000000-2240-22002-2-402-200-222-200002-2-2200000000000000000000000000000000
χ7044-4-44-4-44404-40-4400000000000-22-402-2002-240-2200-222-20000-222-200000000000000000000000000000000
χ7144-4-44-4-4440-4404-4000000000002-2042-200-220-4-2200-222-200002-2-2200000000000000000000000000000000
χ7244-4-44-4-4440-4404-4000000000002-20-4-2200-22042-200-222-20000-222-200000000000000000000000000000000
χ7344-4-44-4-4440-4404-400000000000-2204-22002-20-42-2002-2-220000-222-200000000000000000000000000000000
χ7444-4-44-4-4440-4404-400000000000-220-42-2002-204-22002-2-2200002-2-2200000000000000000000000000000000
χ7588888-8-8-8-800000000000000000000000000000000000000000000000004i−4i00000000000000000000000000
χ7688888-8-8-8-80000000000000000000000000000000000000000000000000−4i4i00000000000000000000000000
χ77888-8-8-888-8000000000000000000000000000000000000000000000004-40000000000000000000000000000
χ78888-8-8-888-800000000000000000000000000000000000000000000000-440000000000000000000000000000
χ7988-88-88-88-8000000000000000000000004-40000004-400000000000000000000000000000000000000000000
χ8088-88-88-88-800000000000000000000000-44000000-4400000000000000000000000000000000000000000000
χ8188-8-8888-8-8000000000000000000000004-4000000-4400000000000000000000000000000000000000000000
χ8288-8-8888-8-800000000000000000000000-440000004-400000000000000000000000000000000000000000000
χ8316-160000000800-800000000000000000000000000000000000000000000000004i−4i0000000000000000000000
χ8416-160000000800-80000000000000000000000000000000000000000000000000−4i4i0000000000000000000000
χ8516-160000000-8008000000000000000000000000000000000000000000000004-4000000000000000000000000
χ8616-160000000-800800000000000000000000000000000000000000000000000-44000000000000000000000000

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