Finite Group Databasebeta

← Group #72319731

Character table — Group #72319731

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1122244444488888888888888161616161616161616161616161616161616163232323232323232323232323232323232323232323232326464646464128128128128
order12222224444222222444444442222444444444448888222444444444444488888888444484488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-111-1-11-1-1-1-1111111111111-1-1-1-11-1-1-1-1
χ31111111111111111111111111-1-1111-1-111111111-1-1-1-1-1111-11111111-1-1-1-1-1-1-1-111-1-111111-1-1-1-1
χ41111111111111111111111111-1-1111-1-111111111-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-111-1-11-11-1-1-1-1-1-1-1-1-1111111-1-1-11-11-1
χ6111111111111111111111-1-1-1-11111111-1-1-1-1-1-11111111-11-11-11-1-11-11-1-1-1-1-1-1-1-11111-1-111-1-11-11
χ7111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-11-1-11-11-11111111111-1-111-1-1-1-11-11
χ8111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-11-1-11-111111111111-1-1-1-111-11-11-1
χ911111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1111-1111111111-1-111-1-1-1-111-1-1-1-1-111-1-1
χ1011111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-11-1-1-11-1-1-1-111-1-111-1-1-1-1111111-1-1-111
χ1111111111111-1-1-1-111-1-1-1-11111-1-1111-1-111-1-1-1-1111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111
χ1211111111111-1-1-1-111-1-1-1-11111-1-1111-1-111-1-1-1-11111111-1-111-1-11-1-1-1-1-1-111-1-111-1-1-1-11111-111-1-1
χ1311111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-11-1-1-11-1-11-11-1-1-111-1-111-1-111-1-11111-1-11
χ1411111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-11-1-1-11-1-11-11-1-111-1-111-1-11111-1-11-111-1
χ1511111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111111111-1-111-1-11-11-111-1-111-1-1-1-1-1-1-1-1111-111-1
χ1611111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111111111-11-11-11-1-11-1111-1-111-1-1-1-1-1-111-1-111-1-11
χ17222222222220000-2-2000022-2-200-2-2-2002-20000222222-2002-200-2000000-2-200220000000000000
χ18222222222220000-2-2000022-2-200-2-2-2002-2000022-2-2-2-22002200-20000002200-2-20000000000000
χ19222222222220000-2-2000022-2-22222-2222-20000-2-20000000-2000200002200-2-20000-2-2000000000
χ20222222222220000-2-2000022-2-2-2-222-2-2-22-20000-2-20000000-200020000-2-20022000022000000000
χ21222222222220000-2-20000-2-22200-2-2-200-220000222222-200-2-20020000002200-2-20000000000000
χ22222222222220000-2-20000-2-22200-2-2-200-22000022-2-2-2-2200-22002000000-2-200220000000000000
χ23222222222220000-2-20000-2-2222222-222-220000-2-200000002000-20000-2-200220000-2-2000000000
χ24222222222220000-2-20000-2-222-2-222-2-2-2-220000-2-200000002000-200002200-2-2000022000000000
χ25222222222222222222222222200-2-2200222222-2-20000000-2000-2000000000000-2-2000000-20000
χ26222222222222222222222-2-2-2-200-2-2200-2-2-2-2-2-2-2-2000000020002000000000000-2-200000020000
χ2722222222222-2-2-2-222-2-2-2-2222200-2-220022-2-2-2-2-2-20000000-2000-20000000000002200000020000
χ2822222222222-2-2-2-222-2-2-2-2-2-2-2-200-2-2200-2-22222-2-200000002000200000000000022000000-20000
χ2922222-2-22-2-2222-2-22222-2-20000002-2-2000000002-20000002000-20020-2000000002-200002-200000
χ3022222-2-22-2-2222-2-22222-2-20000002-2-2000000002-2000000-2000200-202000000002-20000-2200000
χ3122222-2-22-2-2222-2-22222-2-2000000-22-200000000-22000002000-20020-2000000000-22002-20000000
χ3222222-2-22-2-2222-2-22222-2-2000000-22-200000000-2200000-2000200-202000000000-2200-220000000
χ3322222-2-22-2-22-2-22222-2-2220000002-2-2000000002-20000002000-20020-200000000-220000-2200000
χ3422222-2-22-2-22-2-22222-2-2220000002-2-2000000002-2000000-2000200-20200000000-2200002-200000
χ3522222-2-22-2-22-2-22222-2-222000000-22-200000000-22000002000-20020-20000000002-200-220000000
χ3622222-2-22-2-22-2-22222-2-222000000-22-200000000-2200000-2000200-2020000000002-2002-20000000
χ374444444-4-4-4-4000000000044000000000-40000000000002-2002-20-22-22000000000000000000000
χ384444444-4-4-4-4000000000044000000000-4000000000000-2200-2202-22-2000000000000000000000
χ394444444-4-4-4-40000000000-4-400000000040000000000002200220-2-2-2-2000000000000000000000
χ404444444-4-4-4-40000000000-4-40000000004000000000000-2-200-2-202222000000000000000000000
χ4144444-4-44-4-440000-4-400000000004-4400000000-440000000000000000000000000000000000000
χ4244444-4-44-4-440000-4-40000000000-444000000004-40000000000000000000000000000000000000
χ4344444-4-4-444-40000000000004400000000-4000000000002200-2-20-2-222000000000000000000000
χ4444444-4-4-444-40000000000004400000000-400000000000-2-20022022-2-2000000000000000000000
χ4544444-4-4-444-4000000000000-4-4000000004000000000002-200-220-222-2000000000000000000000
χ4644444-4-4-444-4000000000000-4-400000000400000000000-22002-202-2-22000000000000000000000
χ47444-4-44-400002-22-2002-22-24i−4i0022000-2-2002i2i−2i−2i0022-2-20000000000002i−2i00002i−2i0000000000000
χ48444-4-44-400002-22-2002-22-24i−4i00-2-200022002i2i−2i−2i00-2-222000000000000−2i2i0000−2i2i0000000000000
χ49444-4-44-400002-22-2002-22-2−4i4i0022000-2-200−2i−2i2i2i0022-2-2000000000000−2i2i0000−2i2i0000000000000
χ50444-4-44-400002-22-2002-22-2−4i4i00-2-20002200−2i−2i2i2i00-2-2220000000000002i−2i00002i−2i0000000000000
χ51444-4-44-40000-22-2200-22-224i−4i0022000-2-200−2i−2i2i2i00-2-2220000000000002i−2i0000−2i2i0000000000000
χ52444-4-44-40000-22-2200-22-224i−4i00-2-20002200−2i−2i2i2i0022-2-2000000000000−2i2i00002i−2i0000000000000
χ53444-4-44-40000-22-2200-22-22−4i4i0022000-2-2002i2i−2i−2i00-2-222000000000000−2i2i00002i−2i0000000000000
χ54444-4-44-40000-22-2200-22-22−4i4i00-2-200022002i2i−2i−2i0022-2-20000000000002i−2i0000−2i2i0000000000000
χ5544-44-400-4004004-44-400-4400002-20002-2000000002-22-22000-2000000000000000002-2000000000
χ5644-44-400-4004004-44-400-440000-22000-2200000000-22-22-2000200000000000000000-22000000000
χ5744-44-400-400400-444-4004-400002-20002-200000000-22-22-20002000000000000000002-2000000000
χ5844-44-400-400400-444-4004-40000-22000-22000000002-22-22000-200000000000000000-22000000000
χ5944-44-400-40044-400-44-440000002-20002-200000000-22-222000-200000000000000000-22000000000
χ6044-44-400-40044-400-44-44000000-22000-22000000002-22-2-20002000000000000000002-2000000000
χ6144-44-400-4004-4400-444-40000002-20002-2000000002-22-2-2000200000000000000000-22000000000
χ6244-44-400-4004-4400-444-4000000-22000-2200000000-22-222000-2000000000000000002-2000000000
χ6344-4-44000-44022-2-200-2-222004-42-2000-22002-22-200-222-2000000000000002-22-2000000000000000
χ6444-4-44000-44022-2-200-2-222004-4-220002-2002-22-2002-2-2200000000000000-22-22000000000000000
χ6544-4-44000-44022-2-200-2-22200-442-2000-2200-22-2200-222-200000000000000-22-22000000000000000
χ6644-4-44000-44022-2-200-2-22200-44-220002-200-22-22002-2-22000000000000002-22-2000000000000000
χ6744-4-44000-440-2-2220022-2-2004-42-2000-2200-22-22002-2-2200000000000000-222-2000000000000000
χ6844-4-44000-440-2-2220022-2-2004-4-220002-200-22-2200-222-2000000000000002-2-22000000000000000
χ6944-4-44000-440-2-2220022-2-200-442-2000-22002-22-2002-2-22000000000000002-2-22000000000000000
χ7044-4-44000-440-2-2220022-2-200-44-220002-2002-22-200-222-200000000000000-222-2000000000000000
χ71888-8-8-8800004-4-44004-4-4400000000000000000000000000000000000000000000000000000000
χ72888-8-8-880000-444-400-444-400000000000000000000000000000000000000000000000000000000
χ7388-88-800800-8000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000
χ7488-88-800800-800000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ7588-8-880008-80444400-4-4-4-400000000000000000000000000000000000000000000000000000000
χ7688-8-880008-80-4-4-4-400444400000000000000000000000000000000000000000000000000000000
χ7732-32000000000000000000000000000000000000000000000000000000000000000000000000000

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