Finite Group Databasebeta

← Group #72337639

Character table — Group #72337639

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1124444444888888888888881616161616161616161616161632323232323232323264646464646464646464646464646464646464646464
order12222222222222222222224424444444444442444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-11-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-11-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111-1-111-1-1-1-11-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111-1-111-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-11-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-11-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-11-1-111-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-11-1-111-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-22222-2-2-2-2-2-2-22-222-2-200220000200-2-200002-2000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-2-22-222-2-200-2-20000-200220000-22000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-2-22-2-2-22200220000200-2-20000-22000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-2-22-2-2-22200-2-20000-2002200002-2000000000000000000
χ212222222222-2-22222-2-222-2-2-2-2-2-222-22-2220000020-2-200002-200000000000000000000
χ222222222222-2-22222-2-222-2-2-2-2-2-222-22-2-2-200000-20220000-2200000000000000000000
χ232222222222-2-222-2-222-2-222-2-2-2-22-22-22220000020-2-20000-2200000000000000000000
χ242222222222-2-222-2-222-2-222-2-2-2-22-22-22-2-200000-202200002-200000000000000000000
χ252222222222-2-2-2-222-2-2-2-222222-2-22-2-220000222000000-2-200002-20000000000000000
χ262222222222-2-2-2-222-2-2-2-222222-2-22-2-220000-2-2-2000000220000-220000000000000000
χ272222222222-2-2-2-2-2-22222-2-2222-2-2-222-20000222000000-2-20000-220000000000000000
χ282222222222-2-2-2-2-2-22222-2-2222-2-2-222-20000-2-2-20000002200002-20000000000000000
χ29444444-4-4-4-400000000004400000000-40000000000000000000000000000000002-22-2
χ30444444-4-4-4-400000000004400000000-4000000000000000000000000000000000-22-22
χ31444444-4-4-4-40000000000-4-40000000040000000000000000000000000000000002i−2i−2i2i
χ32444444-4-4-4-40000000000-4-4000000004000000000000000000000000000000000−2i2i2i−2i
χ334444-4-444-4-40000000044000000000-4000000000000000000000000002-22-200000000
χ344444-4-444-4-40000000044000000000-400000000000000000000000000-22-2200000000
χ354444-4-444-4-400000000-4-40000000004000000000000000000000000002i−2i−2i2i00000000
χ364444-4-444-4-400000000-4-4000000000400000000000000000000000000−2i2i2i−2i00000000
χ374444-4-4-4-444440000000000000-40000000440000-40000000000000000000000000000
χ384444-4-4-4-444440000000000000-40000000-4-4000040000000000000000000000000000
χ394444-4-4-4-444-4-40000000000000400000000000000004-4000000000000000000000000
χ404444-4-4-4-444-4-4000000000000040000000000000000-44000000000000000000000000
χ41444-44-44-44-4000000440000000000-400000000000000000000000000000002-22-20000
χ42444-44-44-44-4000000440000000000-40000000000000000000000000000000-22-220000
χ43444-44-44-44-4000000-4-40000000000400000000000000000000000000000002i−2i−2i2i0000
χ44444-44-44-44-4000000-4-4000000000040000000000000000000000000000000−2i2i2i−2i0000
χ45444-44-4-44-440044000000000000-400004400000-400000000000000000000000000000
χ46444-44-4-44-440044000000000000-40000-4-400000400000000000000000000000000000
χ47444-44-4-44-4400-4-4000000000000400000000000004-400000000000000000000000000
χ48444-44-4-44-4400-4-400000000000040000000000000-4400000000000000000000000000
χ49444-4-444-4-4400000000000044-4000000000044-4000000000000000000000000000000
χ50444-4-444-4-4400000000000044-40000000000-4-44000000000000000000000000000000
χ51444-4-444-4-44000000000000-4-4400000000000000000004-40000000000000000000000
χ52444-4-444-4-44000000000000-4-440000000000000000000-440000000000000000000000
χ53444-4-44-444-400004400000000000-40000000000000000000000002-22-2000000000000
χ54444-4-44-444-400004400000000000-4000000000000000000000000-22-22000000000000
χ55444-4-44-444-40000-4-40000000000040000000000000000000000002i−2i−2i2i000000000000
χ56444-4-44-444-40000-4-4000000000004000000000000000000000000−2i2i2i−2i000000000000
χ5788-800000004-44-44-44-44-44-44-400000000000000000000000000000000000000000000
χ5888-800000004-44-4-44-44-44-444-400000000000000000000000000000000000000000000
χ5988-800000004-4-444-44-4-44-44-4400000000000000000000000000000000000000000000
χ6088-800000004-4-44-44-444-44-4-4400000000000000000000000000000000000000000000
χ6188-80000000-444-44-4-444-4-44-4400000000000000000000000000000000000000000000
χ6288-80000000-444-4-444-4-444-4-4400000000000000000000000000000000000000000000
χ6388-80000000-44-444-4-44-444-44-400000000000000000000000000000000000000000000
χ6488-80000000-44-44-444-44-4-444-400000000000000000000000000000000000000000000
χ6516-16000000000000000000000000000004i−4i4i−4i4-40000000000000000000000000000000
χ6616-16000000000000000000000000000004i−4i−4i4i-440000000000000000000000000000000
χ6716-1600000000000000000000000000000−4i4i4i−4i-440000000000000000000000000000000
χ6816-1600000000000000000000000000000−4i4i−4i4i4-40000000000000000000000000000000

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