Finite Group Databasebeta

← Group #72219530

Character table — Group #72219530

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222444444888888888888881616161616161616161616161616161616323232323232323232323232323232323264646464646464646464646464128128
order12222224444222222444444442222244448888888822244444444448888488888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-11111-1iiii−i−i−i−iii−i−ii−i
χ6111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-11111-1−i−i−i−iiiii−i−iii−ii
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-1-1iiii−i−i−i−i−i−iii−ii
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-1-1−i−i−i−iiiiiii−i−ii−i
χ91111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-11-111-111-1-111-1-111-1-1-111-1-111-1-11111-1-1
χ101111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-11-111-111-1-111-1-111-1-1-1-1-111-1-111-1-1-1-111
χ111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-11111-111-1111-1-1-1-111-1-111-111-1-111-1-1-1-1-1-111
χ121111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-11111-111-1111-1-1-1-111-1-111-1-1-111-1-1111111-1-1
χ131111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1-11-1-1111-1-1-1-11111-1-11ii−i−i−i−iiiii−i−i−ii
χ141111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1-11-1-1111-1-1-1-11111-1-11−i−iiiii−i−i−i−iiii−i
χ151111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-111111-1-11-111-1-111-1-1-1-1111ii−i−i−i−iii−i−iiii−i
χ161111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-111111-1-11-111-1-111-1-1-1-1111−i−iiiii−i−iii−i−i−ii
χ1722222222222222222222222222222222-2-20000000000-200-2-2-2-200000000-200000000000000
χ18222222222222222222222-2-2-2-22-2-2-2-2-2-2220000000000200-2-2-2-200000000200000000000000
χ192222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-20000000000-200-2-22200000000200000000000000
χ202222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-22222220000000000200-2-22200000000-200000000000000
χ2122222222222-2-20000000022-2-2-22-2000022000022220-2-20-22-200002200-2-2000000000000000
χ2222222222222-2-20000000022-2-2-22-20000220000-2-2-2-202-2022-20000-2-20022000000000000000
χ2322222222222-2-20000000022-2-2-22-20000-2-22222000020220-2200-2-200-2-200000000000000000
χ2422222222222-2-20000000022-2-2-22-20000-2-2-2-2-2-20000-202-20-220022002200000000000000000
χ2522222222222-2-200000000-2-222-2-2200002222220000-20-2-20-22002200-2-200000000000000000
χ2622222222222-2-200000000-2-222-2-22000022-2-2-2-2000020-220-2200-2-2002200000000000000000
χ2722222222222-2-200000000-2-222-2-220000-2-200002222022022-20000-2-200-2-2000000000000000
χ2822222222222-2-200000000-2-222-2-220000-2-20000-2-2-2-20-220-22-20000220022000000000000000
χ294444444-4-4-4-44444-4-444-4-40000-4000000000000000000000000000000000000000000000000
χ304444444-4-4-4-444-4-444-4-4440000-4000000000000000000000000000000000000000000000000
χ314444444-4-4-4-4-4-40000000000004000000000000000000000004-400000000000000000000000
χ324444444-4-4-4-4-4-4000000000000400000000000000000000000-4400000000000000000000000
χ3344444-4-44-44-40000000000004400-4000000000000000000000000000000002-2002-200000000
χ3444444-4-44-44-40000000000004400-400000000000000000000000000000000-2200-2200000000
χ3544444-4-44-44-4000000000000-4-4004000000000000000000000000000000002i−2i00−2i2i00000000
χ3644444-4-44-44-4000000000000-4-400400000000000000000000000000000000−2i2i002i−2i00000000
χ3744444-4-4-44-44000000000044000-4000000000000000000000000000000000002-2002-2000000
χ3844444-4-4-44-44000000000044000-400000000000000000000000000000000000-2200-22000000
χ3944444-4-4-44-440000000000-4-40004000000000000000000000000000000000002i−2i00−2i2i000000
χ4044444-4-4-44-440000000000-4-4000400000000000000000000000000000000000−2i2i002i−2i000000
χ41444-4-4000-404002-22-22-22-24-4000002-22-20022-2-222-2-2200-200000002-20000000000000000000
χ42444-4-4000-404002-22-22-22-24-4000002-22-200-2-222-2-222-20020000000-220000000000000000000
χ43444-4-4000-404002-22-22-22-2-4400000-22-220022-2-222-2-2-20020000000-220000000000000000000
χ44444-4-4000-404002-22-22-22-2-4400000-22-2200-2-222-2-222200-200000002-20000000000000000000
χ45444-4-4000-40400-22-22-22-224-400000-22-220022-2-2-2-222200-20000000-220000000000000000000
χ46444-4-4000-40400-22-22-22-224-400000-22-2200-2-22222-2-2-200200000002-20000000000000000000
χ47444-4-4000-40400-22-22-22-22-44000002-22-20022-2-2-2-222-200200000002-20000000000000000000
χ48444-4-4000-40400-22-22-22-22-44000002-22-200-2-22222-2-2200-20000000-220000000000000000000
χ4944-44-400-4040002-22-2-22-22004-40002-2-22002-22-22-22-20200-200002-2000000000000000000000
χ5044-44-400-4040002-22-2-22-22004-40002-2-2200-22-22-22-220-20020000-22000000000000000000000
χ5144-44-400-4040002-22-2-22-2200-44000-222-2002-22-22-22-20-20020000-22000000000000000000000
χ5244-44-400-4040002-22-2-22-2200-44000-222-200-22-22-22-220200-200002-2000000000000000000000
χ5344-44-400-404000-22-222-22-2004-4000-222-2002-22-2-22-220-200200002-2000000000000000000000
χ5444-44-400-404000-22-222-22-2004-4000-222-200-22-222-22-20200-20000-22000000000000000000000
χ5544-44-400-404000-22-222-22-200-440002-2-22002-22-2-22-220200-20000-22000000000000000000000
χ5644-44-400-404000-22-222-22-200-440002-2-2200-22-222-22-20-200200002-2000000000000000000000
χ5744-4-44-4400004-4004400-4-400000000000002-2-222-2-2200000000000002-22-2000000000000000
χ5844-4-44-4400004-4004400-4-40000000000000-222-2-222-20000000000000-22-22000000000000000
χ5944-4-44-4400004-400-4-4004400000000000002-2-22-222-200000000000002-2-22000000000000000
χ6044-4-44-4400004-400-4-400440000000000000-222-22-2-220000000000000-222-2000000000000000
χ6144-4-44-440000-444400-4-40000000000000002-2-222-2-220000000000000-22-22000000000000000
χ6244-4-44-440000-444400-4-4000000000000000-222-2-222-200000000000002-22-2000000000000000
χ6344-4-44-440000-44-4-400440000000000000002-2-22-222-20000000000000-222-2000000000000000
χ6444-4-44-440000-44-4-40044000000000000000-222-22-2-2200000000000002-2-22000000000000000
χ65888-8-800080-8004-4-444-4-4400000000000000000000000000000000000000000000000000000
χ66888-8-800080-800-444-4-444-400000000000000000000000000000000000000000000000000000
χ6788-88-80080-80004-4-44-444-400000000000000000000000000000000000000000000000000000
χ6888-88-80080-8000-444-44-4-4400000000000000000000000000000000000000000000000000000
χ6988-8-888-800000000000000000000044-4-4000000000000000000000000000000000000000000
χ7088-8-888-8000000000000000000000-4-444000000000000000000000000000000000000000000
χ7116-160000000000000000000000000000004-400000000000000000000000000000000002i−2i2i−2i00
χ7216-160000000000000000000000000000004-40000000000000000000000000000000000−2i2i−2i2i00
χ7316-16000000000000000000000000000000-4400000000000000000000000000000000002-2-2200
χ7416-16000000000000000000000000000000-440000000000000000000000000000000000-222-200

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