Finite Group Databasebeta

← Group #10823680

Character table — Group #10823680

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444666666668888888888888888881616161616161616161616162424242424242424242424242424
order122222344446666612121212444444442244444444888812121212661212121212122424242444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-11-1-1-111-1-111-1-1-1-1-1-11-1-1-11-11111-1-11-1-1-11-111-1-111-1-1
χ411111111111111111111111111111-11-1-1-1-1-111-1-11111111-1-1-11-1-1-1-1-1111-1-1-11-1-1-111-1-111
χ51111111111111111111111111111-11-11-1-111-1-1-1-111-1-1-1-1-11-1-1-1111-1-111-11-1-1-1111-1-1-1-111
χ61111111111111111111111111111-11-11-1-1-1-11111-1-11111-11-1-1-11-1-111-1-1-11-1-1-11-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-1-1-11-1-1-11-11111-1-1-1111-11-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-11111111-1-1-11-1-1-1-1-111-1111-1111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-111-1-1-1-1-11-1-1-1111-1-1111-1111-1-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-11111-11-1-1-11-1-111-1-11-1111-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1-1-1
χ172222222-2-2-2-222222-2-2-2-22222-2-2-2-200002-2000000000000002-200000000002-20000000000
χ182222222-2-2-2-222222-2-2-2-22222-2-2-2-20000-2200000000000000-220000000000-220000000000
χ192222222-2-2-2-222222-2-2-2-2-2-2-2-2222200002-2000000000000002-20000000000-220000000000
χ202222222-2-2-2-222222-2-2-2-2-2-2-2-222220000-2200000000000000-2200000000002-20000000000
χ21222222-12222-1-1-1-1-1-1-1-1-10000000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-100000000222222-2-2-2-2-2-2-2-21111-1-1-1-1-1-111111100000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-1000000002-22-2-2-222-2-222-2-21111-1111-11-1-1-1-11100000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-1000000002-22-2-2-2-2-222-2-222-1-1-1-1-1111-111111-1-100000000000000
χ25222222-12222-1-1-1-1-1-1-1-1-100000000-22-22-2-222-2-2-2-22211111-1111-1-1-111-1-100000000000000
χ26222222-12222-1-1-1-1-1-1-1-1-100000000-22-22-2-2-2-22222-2-2-1-1-1-11-1111-111-1-11100000000000000
χ27222222-12222-1-1-1-1-1-1-1-1-100000000-2-2-2-2222222-2-2-2-2-1-1-1-111-1-111-1-1111100000000000000
χ28222222-12222-1-1-1-1-1-1-1-1-100000000-2-2-2-222-2-2-2-22222111111-1-11111-1-1-1-100000000000000
χ292222-2-222-22-2222-2-22-22-222-2-222-2-2020-20000000000000002000-200000002000-200000000
χ302222-2-222-22-2222-2-22-22-222-2-222-2-20-202000000000000000-200020000000-2000200000000
χ312222-2-222-22-2222-2-22-22-2-2-222-2-222020-20000000000000002000-20000000-2000200000000
χ322222-2-222-22-2222-2-22-22-2-2-222-2-2220-202000000000000000-2000200000002000-200000000
χ332222-2-22-22-22222-2-2-22-2222-2-2-2-22220-20000000000000002000-20000000-20002000000000
χ342222-2-22-22-22222-2-2-22-2222-2-2-2-222-202000000000000000-2000200000002000-2000000000
χ352222-2-22-22-22222-2-2-22-22-2-22222-2-220-20000000000000002000-200000002000-2000000000
χ362222-2-22-22-22222-2-2-22-22-2-22222-2-2-202000000000000000-200020000000-20002000000000
χ3722-2-22-222-2-22-2-22-22-222-22i−2i2i−2i2i−2i2i−2i0000000000002-2000000000000002-20000000000002i−2i
χ3822-2-22-222-2-22-2-22-22-222-22i−2i2i−2i2i−2i2i−2i000000000000-2200000000000000-22000000000000−2i2i
χ3922-2-22-222-2-22-2-22-22-222-2−2i2i−2i2i−2i2i−2i2i0000000000002-2000000000000002-2000000000000−2i2i
χ4022-2-22-222-2-22-2-22-22-222-2−2i2i−2i2i−2i2i−2i2i000000000000-2200000000000000-220000000000002i−2i
χ4122-2-22-22-222-2-2-22-222-2-222i−2i2i−2i−2i2i−2i2i00000000002-2000000000000002-20000000000002i−2i00
χ4222-2-22-22-222-2-2-22-222-2-222i−2i2i−2i−2i2i−2i2i0000000000-2200000000000000-22000000000000−2i2i00
χ4322-2-22-22-222-2-2-22-222-2-22−2i2i−2i2i2i−2i2i−2i00000000002-2000000000000002-2000000000000−2i2i00
χ4422-2-22-22-222-2-2-22-222-2-22−2i2i−2i2i2i−2i2i−2i0000000000-2200000000000000-220000000000002i−2i00
χ4522-2-2-22222-2-2-2-222-2-2-2222i−2i−2i2i2i−2i−2i2i0000002-200000000000000002-200000000002i−2i000000
χ4622-2-2-22222-2-2-2-222-2-2-2222i−2i−2i2i2i−2i−2i2i000000-220000000000000000-220000000000−2i2i000000
χ4722-2-2-22222-2-2-2-222-2-2-222−2i2i2i−2i−2i2i2i−2i0000002-200000000000000002-20000000000−2i2i000000
χ4822-2-2-22222-2-2-2-222-2-2-222−2i2i2i−2i−2i2i2i−2i000000-220000000000000000-2200000000002i−2i000000
χ4922-2-2-222-2-222-2-222-222-2-22i−2i−2i2i−2i2i2i−2i000000002i−2i00002i2i−2i−2i000000000000000000002-20000
χ5022-2-2-222-2-222-2-222-222-2-22i−2i−2i2i−2i2i2i−2i00000000−2i2i0000−2i−2i2i2i00000000000000000000-220000
χ5122-2-2-222-2-222-2-222-222-2-2−2i2i2i−2i2i−2i−2i2i000000002i−2i00002i2i−2i−2i00000000000000000000-220000
χ5222-2-2-222-2-222-2-222-222-2-2−2i2i2i−2i2i−2i−2i2i00000000−2i2i0000−2i−2i2i2i000000000000000000002-20000
χ53444444-2-4-4-4-4-2-2-2-2-222220000000000004-400000000000000-220000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-22222000000000000-44000000000000002-20000000000000000000000
χ554444-4-4-24-44-4-2-2-222-22-2200000000040-4000000000000000-2000200000000000000000000
χ564444-4-4-24-44-4-2-2-222-22-22000000000-4040000000000000002000-200000000000000000000
χ574444-4-4-2-44-44-2-2-2222-22-20000000040-4000000000000000-20002000000000000000000000
χ584444-4-4-2-44-44-2-2-2222-22-200000000-4040000000000000002000-2000000000000000000000
χ5944-4-44-4-24-4-4422-22-22-2-22000000000000000000004-400000000000000-2200000000000000
χ6044-4-44-4-24-4-4422-22-22-2-2200000000000000000000-44000000000000002-200000000000000
χ6144-4-44-4-2-444-422-22-2-222-20000000000000000004-400000000000000-220000000000000000
χ6244-4-44-4-2-444-422-22-2-222-2000000000000000000-44000000000000002-20000000000000000
χ6344-4-4-44-244-4-422-2-2222-2-2000000000000004-40000000000000000-22000000000000000000
χ6444-4-4-44-244-4-422-2-2222-2-200000000000000-4400000000000000002-2000000000000000000
χ6544-4-4-44-2-4-44422-2-22-2-22200000000000000004i−4i0000−2i−2i2i2i00000000000000000000000000
χ6644-4-4-44-2-4-44422-2-22-2-2220000000000000000−4i4i00002i2i−2i−2i00000000000000000000000000
χ678-88-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ688-88-800-400004-44000000000000000000000000000023−2323−2300000000000000000000000000
χ698-88-800-400004-440000000000000000000000000000−2323−232300000000000000000000000000
χ708-8-8800800008-8-80000000000000000000000000000000000000000000000000000000000
χ718-8-8800-40000-4440000000000000000000000000000−2i32i32i3−2i300000000000000000000000000
χ728-8-8800-40000-44400000000000000000000000000002i3−2i3−2i32i300000000000000000000000000

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