Finite Group Databasebeta

← Group #72262257

Character table — Group #72262257

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222244444444444488888888888816161616161616161616161616161616161616161616161616161616161632323232323232323232323264646464646464646464646464646464
order12222222222222222222222222222244442222222222444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111111111111111-1-1-1-11111-1-111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111111111111111-1-1-1-11111-1-111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222222-2-2-2-22222-2-2-2-22222-2-20000-2-222-2-2000000000000-2-222-2-2000000000000000000000000
χ182222222222222222222222-2-2-2-22222-2-2-2-222-2-2220000-2-2-2-222000000000000-2-2-2-222000000000000000000000000
χ192222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-200002222-2-200000000000022-2-222000000000000000000000000
χ202222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222000022-2-2220000000000002222-2-2000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22-2000022-2-22-2000022-2-2000000002-2000022-2-200000000000000000000
χ22222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22-20000-2-2222-20000-2-222000000002-20000-2-22200000000000000000000
χ23222222222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-2-22000022-2-2-22000022-2-200000000-220000-2-22200000000000000000000
χ24222222222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-2-220000-2-222-220000-2-22200000000-22000022-2-200000000000000000000
χ25222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222222-200000000-22000000002222-2-2-2-2-220000000022-2-20000000000000000
χ26222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222222-200000000-2200000000-2-2-2-22222-2200000000-2-2220000000000000000
χ27222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222-22000000002-2000000002222-2-2-2-22-200000000-2-2220000000000000000
χ28222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222-22000000002-200000000-2-2-2-222222-20000000022-2-20000000000000000
χ292222-2-2-222-22-22222-2-2-2-22-222-2-2222222-2-2-2-2000000002-20000000000000000-2200000000000000002-22-200000000
χ302222-2-2-222-22-22222-2-2-2-22-222-2-2222222-2-2-2-2000000002-20000000000000000-220000000000000000-22-2200000000
χ312222-2-2-222-22-22222-2-2-2-22-222-2-2-2-2-2-222-2-22200000000-2200000000000000002-200000000000000002i−2i−2i2i00000000
χ322222-2-2-222-22-22222-2-2-2-22-222-2-2-2-2-2-222-2-22200000000-2200000000000000002-20000000000000000−2i2i2i−2i00000000
χ332222-2-2-222-22-22222-2-2-2-22-2-2-2222222-2-222-2-200000000-2200000000000000002-20000000000002-22-2000000000000
χ342222-2-2-222-22-22222-2-2-2-22-2-2-2222222-2-222-2-200000000-2200000000000000002-2000000000000-22-22000000000000
χ352222-2-2-222-22-22222-2-2-2-22-2-2-222-2-2-2-2-2-22222000000002-20000000000000000-220000000000002i−2i−2i2i000000000000
χ362222-2-2-222-22-22222-2-2-2-22-2-2-222-2-2-2-2-2-22222000000002-20000000000000000-22000000000000−2i2i2i−2i000000000000
χ372222-2-2-222-22-2-2-2-2-222222-222-2-222-2-2-2-222-2200000000220000000000000000-2-20000000000000000000000002i−2i2i−2i
χ382222-2-2-222-22-2-2-2-2-222222-222-2-222-2-2-2-222-2200000000220000000000000000-2-2000000000000000000000000−2i2i−2i2i
χ392222-2-2-222-22-2-2-2-2-222222-222-2-2-2-222-2-2222-200000000-2-20000000000000000220000000000000000000000002-2-22
χ402222-2-2-222-22-2-2-2-2-222222-222-2-2-2-222-2-2222-200000000-2-2000000000000000022000000000000000000000000-222-2
χ412222-2-2-222-22-2-2-2-2-222222-2-2-22222-2-222-2-2-2200000000-2-2000000000000000022000000000000000000002-22-20000
χ422222-2-2-222-22-2-2-2-2-222222-2-2-22222-2-222-2-2-2200000000-2-200000000000000002200000000000000000000-22-220000
χ432222-2-2-222-22-2-2-2-2-222222-2-2-222-2-22222-2-22-200000000220000000000000000-2-2000000000000000000002i−2i−2i2i0000
χ442222-2-2-222-22-2-2-2-2-222222-2-2-222-2-22222-2-22-200000000220000000000000000-2-200000000000000000000−2i2i2i−2i0000
χ454444444444-4-444-4-444-4-4-4-400000000000000004400000000-4-4000000000000000000000000000000000000000000
χ464444444444-4-444-4-444-4-4-4-40000000000000000-4-40000000044000000000000000000000000000000000000000000
χ474444444444-4-4-4-444-4-444-4-4000000000000004400000000-4-400000000000000000000000000000000000000000000
χ484444444444-4-4-4-444-4-444-4-400000000000000-4-4000000004400000000000000000000000000000000000000000000
χ49444444-4-4-4-44400000000-4-4000000004-44-400000000000000000000000000000000000000004i−4i0000000000000000
χ50444444-4-4-4-44400000000-4-4000000004-44-40000000000000000000000000000000000000000−4i4i0000000000000000
χ51444444-4-4-4-44400000000-4-400000000-44-44000000000000000000000000000000000000004i−4i000000000000000000
χ52444444-4-4-4-44400000000-4-400000000-44-4400000000000000000000000000000000000000−4i4i000000000000000000
χ53444444-4-4-4-4-4-400000000444-44-4000000000000000000000000000000000000000000004-400000000000000000000
χ54444444-4-4-4-4-4-400000000444-44-400000000000000000000000000000000000000000000-4400000000000000000000
χ55444444-4-4-4-4-4-40000000044-44-440000000000000000000000000000000000000000004-40000000000000000000000
χ56444444-4-4-4-4-4-40000000044-44-44000000000000000000000000000000000000000000-440000000000000000000000
χ574444-4-44-4-444-400000000-44000000004-4-440000000000000000000044-4-40000000000000000000000000000000000
χ584444-4-44-4-444-400000000-44000000004-4-4400000000000000000000-4-4440000000000000000000000000000000000
χ594444-4-44-4-444-400000000-4400000000-444-400000000000000000000000044-4-4000000000000000000000000000000
χ604444-4-44-4-444-400000000-4400000000-444-4000000000000000000000000-4-444000000000000000000000000000000
χ614444-4-44-4-44-44000000004-44-4-44000000000000004400000000-4-40000000000000000000000000000000000000000
χ624444-4-44-4-44-44000000004-44-4-4400000000000000-4-400000000440000000000000000000000000000000000000000
χ634444-4-44-4-44-44000000004-4-444-400000000000000004400000000-4-400000000000000000000000000000000000000
χ644444-4-44-4-44-44000000004-4-444-40000000000000000-4-4000000004400000000000000000000000000000000000000
χ654444-4-4-444-4-4444-4-4-4-444-44000000000000000000000000000000000000000000004-4000000000000000000000000
χ664444-4-4-444-4-4444-4-4-4-444-4400000000000000000000000000000000000000000000-44000000000000000000000000
χ674444-4-4-444-4-44-4-44444-4-4-440000000000000000000000000000000000000000004-400000000000000000000000000
χ684444-4-4-444-4-44-4-44444-4-4-44000000000000000000000000000000000000000000-4400000000000000000000000000
χ694-4-444-4-44-4400004-4004-4000000000000000000002-22-2004-4002-22-22-22-22-22-2000000000000000000000000000000
χ704-4-444-4-44-4400004-4004-4000000000000000000002-22-200-44002-22-2-22-22-22-22000000000000000000000000000000
χ714-4-444-4-44-4400004-4004-400000000000000000000-22-22004-400-22-22-22-22-22-22000000000000000000000000000000
χ724-4-444-4-44-4400004-4004-400000000000000000000-22-2200-4400-22-222-22-22-22-2000000000000000000000000000000
χ734-4-444-4-44-440000-4400-4400000000000000004-4002-2-220000002-2-222-22-2-22-22000000000000000000000000000000
χ744-4-444-4-44-440000-4400-4400000000000000004-400-222-2000000-222-2-22-222-22-2000000000000000000000000000000
χ754-4-444-4-44-440000-4400-440000000000000000-44002-2-220000002-2-22-22-222-22-2000000000000000000000000000000
χ764-4-444-4-44-440000-4400-440000000000000000-4400-222-2000000-222-22-22-2-22-22000000000000000000000000000000
χ774-4-44-44-4-444004-4004-400000000000000000000002-22-200004-4-22-222-2-222-2-22000000000000000000000000000000
χ784-4-44-44-4-444004-4004-400000000000000000000002-22-20000-44-22-22-222-2-222-2000000000000000000000000000000
χ794-4-44-44-4-444004-4004-40000000000000000000000-22-2200004-42-22-2-222-2-222-2000000000000000000000000000000
χ804-4-44-44-4-444004-4004-40000000000000000000000-22-220000-442-22-22-2-222-2-22000000000000000000000000000000
χ814-4-44-44-4-44400-4400-44000000000000000000004-42-2-22000000-222-22-2-22-222-2000000000000000000000000000000
χ824-4-44-44-4-44400-4400-44000000000000000000004-4-222-20000002-2-22-222-22-2-22000000000000000000000000000000
χ834-4-44-44-4-44400-4400-4400000000000000000000-442-2-22000000-222-2-222-22-2-22000000000000000000000000000000
χ844-4-44-44-4-44400-4400-4400000000000000000000-44-222-20000002-2-222-2-22-222-2000000000000000000000000000000
χ858-8-888-88-88-8008-800-8800000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-88-88-800-88008-800000000000000000000000000000000000000000000000000000000000000000000000000
χ878-8-88-8888-8-800008-800-88000000000000000000000000000000000000000000000000000000000000000000000000
χ888-8-88-8888-8-80000-88008-8000000000000000000000000000000000000000000000000000000000000000000000000
χ891616-16-160000000000000000000000008-800000000000000000000000000000000000000000000000000000000000000
χ901616-16-16000000000000000000000000-8800000000000000000000000000000000000000000000000000000000000000
χ9116-1616-1600000000000000000000008-80000000000000000000000000000000000000000000000000000000000000000
χ9216-1616-160000000000000000000000-880000000000000000000000000000000000000000000000000000000000000000

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