Finite Group Databasebeta

← Group #72238372

Character table — Group #72238372

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size1122244444488888816161616161616161616161616161616161616161632323232323232323232323232323232323232323232326464646464646464646464646464128128128128128128128128128128128128128128128128
order1222222222222222222222224444444444444422244444444444444444444244444444444444488888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-11111-1-1111111111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111
χ7111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111-11-1-11-1111-1-1111-1-1-1-1-11111111-1-1-1-1-111-11-11-111111-1-111iiii−i−i−i−i-1-1-111ii−i−i-1-111-1-1i−i11-1-1i−iii−i−iii−i−i
χ1011111-11-1-11-1111-1-1111-1-1-1-1-11111111-1-1-1-1-111-11-11-111111-1-111−i−i−i−iiiii-1-1-111−i−iii-1-111-1-1−ii11-1-1−ii−i−iii−i−iii
χ1111111-11-1-11-1111-1-1111-1-1-1-1-11111111-1-1-1-1-111-11-11-11-1-111-1-1-1-1iiii−i−i−i−i-111-1-1ii−i−i1111-1-1i−i-1-111i−i−i−iii−i−iii
χ1211111-11-1-11-1111-1-1111-1-1-1-1-11111111-1-1-1-1-111-11-11-11-1-111-1-1-1-1−i−i−i−iiiii-111-1-1−i−iii1111-1-1−ii-1-111−iiii−i−iii−i−i
χ1311111-11-1-11-1111-1-1111-1-1-1-1-11111111-1-1-1-1-111-1-11-11111-1-11111iiii−i−i−i−i-1-1-111ii−i−i-1-1-1-111−ii-1-111−iiii−i−i−i−iii
χ1411111-11-1-11-1111-1-1111-1-1-1-1-11111111-1-1-1-1-111-1-11-11111-1-11111−i−i−i−iiiii-1-1-111−i−iii-1-1-1-111i−i-1-111i−i−i−iiiii−i−i
χ1511111-11-1-11-1111-1-1111-1-1-1-1-11111111-1-1-1-1-111-1-11-111-1-1-1-111-1-1iiii−i−i−i−i-111-1-1ii−i−i11-1-111−ii11-1-1−ii−i−iiiii−i−i
χ1611111-11-1-11-1111-1-1111-1-1-1-1-11111111-1-1-1-1-111-1-11-111-1-1-1-111-1-1−i−i−i−iiiii-111-1-1−i−iii11-1-111i−i11-1-1i−iii−i−i−i−iii
χ17222222222222222222222-2-222-2-2-2-222-2-2222-2-2-20000-20000000022222222-20000-2-2-2-20000000000000000000000
χ18222222222222222222222-2-222-2-2-2-222-2-2222-2-2-20000-200000000-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ19222222222222222222-22222-2-22222-2-2-2-2-2-2-2-2-220000-20000000000000000-2000000000000000000000000002i−2i2i−2i
χ20222222222222222222-22222-2-22222-2-2-2-2-2-2-2-2-220000-20000000000000000-200000000000000000000000000−2i2i−2i2i
χ21222222222222222222-222-2-2-2-2-2-2-2-2-2-222-2-2-222-2000020000000000000000200000000000000002-22-20000000000
χ22222222222222222222-222-2-2-2-2-2-2-2-2-2-222-2-2-222-200002000000000000000020000000000000000-22-220000000000
χ23222222222222-2-2222-22-2-2222222-2-2-2-2222-2-222-22222-20022220000000000-20000000000-2-2-2-20000000000000000
χ24222222222222-2-2222-22-2-2222222-2-2-2-2222-2-222-2-2-2-2-2-200-2-2-2-20000000000-2000000000022220000000000000000
χ25222222222222-2-2222-22-2-2-2-222-2-222-2-2-2-22-2-2-2-22000020000000000000000200000000000000220000-2-200000000
χ26222222222222-2-2222-22-2-2-2-222-2-222-2-2-2-22-2-2-2-22000020000000000000000200000000000000-2-200002200000000
χ27222222222222-2-2222-2-2-2-222-2-222-2-222-2-2-222-2-2-2000020000000000000000200000000000000000000002-22-20000
χ28222222222222-2-2222-2-2-2-222-2-222-2-222-2-2-222-2-2-200002000000000000000020000000000000000000000-22-220000
χ29222222222222-2-2222-2-2-2-2-2-2-2-2-2-2222222-2222220000-2220000-2-200000000-2222-20000-2-200000000000000000000
χ30222222222222-2-2222-2-2-2-2-2-2-2-2-2-2222222-2222220000-2-2-200002200000000-2-2-2-2200002200000000000000000000
χ3122222-22-2-22-2222-2-2222-2-222-22-2-2-2-22222-2-2-2-2-220000-2000000002i2i2i2i−2i−2i−2i−2i20000−2i−2i2i2i0000000000000000000000
χ3222222-22-2-22-2222-2-2222-2-222-22-2-2-2-22222-2-2-2-2-220000-200000000−2i−2i−2i−2i2i2i2i2i200002i2i−2i−2i0000000000000000000000
χ3322222-22-2-22-2222-2-222-2-2-2222-2-2-2-2-2-2-2-2-2222222000020000000000000000-200000000000000002-2-220000000000
χ3422222-22-2-22-2222-2-222-2-2-2222-2-2-2-2-2-2-2-2-2222222000020000000000000000-20000000000000000-222-20000000000
χ3522222-22-2-22-2222-2-222-2-2-2-2-22-22222-2-222222-2-2-20000-200000000000000002000000000000000000000000002-2-22
χ3622222-22-2-22-2222-2-222-2-2-2-2-22-22222-2-222222-2-2-20000-20000000000000000200000000000000000000000000-222-2
χ3722222-22-2-22-22-2-2-2-22-222222-22-2-222-2-222-222-2-2-2000020000000000000000-2000000000000002i−2i0000−2i2i00000000
χ3822222-22-2-22-22-2-2-2-22-222222-22-2-222-2-222-222-2-2-2000020000000000000000-200000000000000−2i2i00002i−2i00000000
χ3922222-22-2-22-22-2-2-2-22-2222-2-2-2222-2-2-2-2-2-2-2222222-22-2-20022-2-2000000000020000000000-2-2220000000000000000
χ4022222-22-2-22-22-2-2-2-22-2222-2-2-2222-2-2-2-2-2-2-222222-22-22-200-2-22200000000002000000000022-2-20000000000000000
χ4122222-22-2-22-22-2-2-2-22-2-222222-2-2-22222-2-22-2-222-20000-2220000-2-2000000002-2-22-200002200000000000000000000
χ4222222-22-2-22-22-2-2-2-22-2-222222-2-2-22222-2-22-2-222-20000-2-2-200002200000000222-220000-2-200000000000000000000
χ4322222-22-2-22-22-2-2-2-22-2-222-2-22-222-2-222222-2-2-2-22000020000000000000000-200000000000000000000002i−2i−2i2i0000
χ4422222-22-2-22-22-2-2-2-22-2-222-2-22-222-2-222222-2-2-2-22000020000000000000000-20000000000000000000000−2i2i2i−2i0000
χ454444444-4-444-4004-4-40400004-400000000-40000000000220000220000000002-2-2-200002-200000000000000000000
χ464444444-4-444-4004-4-40400004-400000000-40000000000-2-20000-2-2000000000-22220000-2200000000000000000000
χ474444444-4-444-4004-4-40-40000-440000000040000000000220000-2-20000000002-2-220000-2200000000000000000000
χ484444444-4-444-4004-4-40-40000-440000000040000000000-2-2000022000000000-222-200002-200000000000000000000
χ49444444-444-44400-4-4-4000000000000004-40004-40000000000000022-2-222-2-2000002-22-20000000000000000000000
χ50444444-444-44400-4-4-4000000000000004-40004-400000000000000-2-222-2-22200000-22-220000000000000000000000
χ51444444-444-44400-4-4-400000000000000-44000-440000000000000022-2-222-2-200000-22-220000000000000000000000
χ52444444-444-44400-4-4-400000000000000-44000-4400000000000000-2-222-2-222000002-22-20000000000000000000000
χ53444444-4-4-4-44-400-4440000000000004-40004-40002222000-2-2-2-20000000000000000000002-22-20000000000000000
χ54444444-4-4-4-44-400-4440000000000004-40004-4000-2-2-2-20002222000000000000000000000-22-220000000000000000
χ55444444-4-4-4-44-400-444000000000000-44000-440002222000-2-2-2-2000000000000000000000-22-220000000000000000
χ56444444-4-4-4-44-400-444000000000000-44000-44000-2-2-2-200022220000000000000000000002-22-20000000000000000
χ5744444-44444-4-400-44-4040000-4-4000000004000000000022000022000000000-22-2-20000-2200000000000000000000
χ5844444-44444-4-400-44-4040000-4-40000000040000000000-2-20000-2-20000000002-22200002-200000000000000000000
χ5944444-44444-4-400-44-40-400004400000000-40000000000220000-2-2000000000-22-2200002-200000000000000000000
χ6044444-44444-4-400-44-40-400004400000000-40000000000-2-20000220000000002-22-20000-2200000000000000000000
χ6144444-4-444-4-4-4004-440000000000004-4000-440002-22-2000-2-2220000000000000000000002-2-220000000000000000
χ6244444-4-444-4-4-4004-440000000000004-4000-44000-22-2200022-2-2000000000000000000000-222-20000000000000000
χ6344444-4-444-4-4-4004-44000000000000-440004-40002-22-2000-2-222000000000000000000000-222-20000000000000000
χ6444444-4-444-4-4-4004-44000000000000-440004-4000-22-2200022-2-20000000000000000000002-2-220000000000000000
χ6544444-4-4-4-4-4-440044-4000000000000004-4000-44000000000000002i2i−2i−2i−2i−2i2i2i00000−2i2i2i−2i0000000000000000000000
χ6644444-4-4-4-4-4-440044-4000000000000004-4000-4400000000000000−2i−2i2i2i2i2i−2i−2i000002i−2i−2i2i0000000000000000000000
χ6744444-4-4-4-4-4-440044-400000000000000-440004-4000000000000002i2i−2i−2i−2i−2i2i2i000002i−2i−2i2i0000000000000000000000
χ6844444-4-4-4-4-4-440044-400000000000000-440004-400000000000000−2i−2i2i2i2i2i−2i−2i00000−2i2i2i−2i0000000000000000000000
χ69888-8-880000-8044000-404-40000000000000000000000000000000004i−4i004i−4i0000000000000000000000000000000
χ70888-8-880000-8044000-404-4000000000000000000000000000000000−4i4i00−4i4i0000000000000000000000000000000
χ71888-8-880000-80-4-400040-4400000000000000000000000000000004i−4i004i−4i000000000000000000000000000000000
χ72888-8-880000-80-4-400040-440000000000000000000000000000000−4i4i00−4i4i000000000000000000000000000000000
χ73888-8-8-800008044000-40-440000000000000000000000000000000004-400-440000000000000000000000000000000
χ74888-8-8-800008044000-40-44000000000000000000000000000000000-44004-40000000000000000000000000000000
χ75888-8-8-8000080-4-4000404-400000000000000000000000000000004-400-44000000000000000000000000000000000
χ76888-8-8-8000080-4-4000404-40000000000000000000000000000000-44004-4000000000000000000000000000000000
χ7788-8-88008-80000000000004-4004-4000000000000040-40004-40000000000000000000000000000000000000000000
χ7888-8-88008-80000000000004-4004-40000000000000-404000-440000000000000000000000000000000000000000000
χ7988-8-88008-8000000000000-4400-4400000000000040-40000004-400000000000000000000000000000000000000000
χ8088-8-88008-8000000000000-4400-44000000000000-404000000-4400000000000000000000000000000000000000000
χ8188-8-8800-880000000000004-400-4400000000000040-4000000-4400000000000000000000000000000000000000000
χ8288-8-8800-880000000000004-400-44000000000000-4040000004-400000000000000000000000000000000000000000
χ8388-8-8800-88000000000000-44004-4000000000000040-4000-440000000000000000000000000000000000000000000
χ8488-8-8800-88000000000000-44004-40000000000000-4040004-40000000000000000000000000000000000000000000
χ851616-1616-1600000000000000000000008-800000000000000000000000000000000000000000000000000000000000000
χ861616-1616-160000000000000000000000-8800000000000000000000000000000000000000000000000000000000000000
χ8716-160000-8008008-80000000000000000000000000000004-400004-4000000000000000000000000000000000000000
χ8816-160000-8008008-8000000000000000000000000000000-440000-44000000000000000000000000000000000000000
χ8916-160000-800800-880000000000000000000000000000004-40000-44000000000000000000000000000000000000000
χ9016-160000-800800-88000000000000000000000000000000-4400004-4000000000000000000000000000000000000000
χ9132-3200001600-16000000000000000000000000000000000000000000000000000000000000000000000000000000000

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