Finite Group Databasebeta

← Group #10827629

Character table — Group #10827629

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444466668888888888881212121212121212121216161616161616161616161616162424242424244848
order1222222222366622226666662222224444446666222222444444661212121212121212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-11-1-1-1-1-11111111111-1-1-1-11-11-1-1-11-111-1-1-1-111-1-1-1-11-1
χ31111111111111111111111111111-11-11-1-1-1-11111111111-1-1-1-1-11-11-1-1-11-1-111-1-1-1-111-1-1-11
χ41111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11-11-1-1-1-1-11111-1-1-1-1-1-111111-11-1-1-11-111-1-1-1-1-1-11111-11
χ7111111111111111111111111-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-11111-11-11-1-1-11-1-111-1-111-1-1111-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111
χ911111111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ1011111111111111-1-1-1-111111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1111111-1-111-11
χ1111111111111111-1-1-1-11111111111-11-11-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1111-1-111-1-111111-1
χ1211111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111
χ1311111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ1411111111111111-1-1-1-1111111-1-1-1-11-11-1-1-111-1-1-1-1-1-111111111-111-1-1-11-1-1-11111-1-111-1-11-1
χ1511111111111111-1-1-1-1111111-1-1-1-1-11-11-1-111-1-1-1-1-1-1111111111-1-11-1-1-1111-1-11111-1-1-1-1-11
χ1611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1111111-1-1
χ172222222222-1-1-1-12222-1-1-1-1-1-1000022222222-1-1-1-1000000000022-1-1-1-1-1-1-1-1-1-1-1-100000000
χ182222222222-1-1-1-12222-1-1-1-1-1-100002-22-2-2-2-2-2-1-1-1-100000000002-2-1111-11-1-1111100000000
χ192222222222-1-1-1-12222-1-1-1-1-1-10000-22-22-2-2-2-2-1-1-1-10000000000-221-1111-111-1-11100000000
χ202222222222-1-1-1-12222-1-1-1-1-1-10000-2-2-2-22222-1-1-1-10000000000-2-211-1-1111111-1-100000000
χ212222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-10000222222-2-211110000000000-2-2-1-1-1-1-1-111111100000000
χ222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-100002-22-2-2-22211110000000000-22-1111-1111-1-1-1-100000000
χ232222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-10000-22-22-2-222111100000000002-21-1111-1-1-111-1-100000000
χ242222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-10000-2-2-2-222-2-2111100000000002211-1-111-1-1-1-11100000000
χ2522222-2-2-2-22222200002-2-22-2-2222200002-2000000-2-2000022-2-200002-20000000000000000
χ2622222-2-2-2-22222200002-2-22-2-222220000-22000000-2-20000-2-2220000-220000000000000000
χ2722222-2-2-2-22222200002-2-22-2-2-2-2-2-200002-2000000220000-2-22200002-20000000000000000
χ2822222-2-2-2-22222200002-2-22-2-2-2-2-2-20000-2200000022000022-2-20000-220000000000000000
χ292222-22-22-2-222220000-22-2-22-222-2-2020-2000000002-2000000000002000-2000000002-20000
χ302222-22-22-2-222220000-22-2-22-222-2-20-202000000002-200000000000-2000200000000-220000
χ312222-22-22-2-222220000-22-2-22-2-2-222020-200000000-22000000000002000-200000000-220000
χ322222-22-22-2-222220000-22-2-22-2-2-2220-20200000000-2200000000000-20002000000002-20000
χ332222-2-22-22-222220000-2-22-2-2222-2-220-2000000000-2200000000002000-200000002-2000000
χ342222-2-22-22-222220000-2-22-2-2222-2-2-202000000000-220000000000-200020000000-22000000
χ352222-2-22-22-222220000-2-22-2-22-2-22220-20000000002-200000000002000-20000000-22000000
χ362222-2-22-22-222220000-2-22-2-22-2-222-2020000000002-20000000000-2000200000002-2000000
χ3722-2-2222-2-2-22-2-2222-2-22-2-2-22200000000000022-2-20000002i−2i2i−2i0000000000000000002i−2i00
χ3822-2-2222-2-2-22-2-2222-2-22-2-2-22200000000000022-2-2000000−2i2i−2i2i000000000000000000−2i2i00
χ3922-2-2222-2-2-22-2-22-2-2222-2-2-222000000000000-2-2220000002i−2i2i−2i000000000000000000−2i2i00
χ4022-2-2222-2-2-22-2-22-2-2222-2-2-222000000000000-2-222000000−2i2i−2i2i0000000000000000002i−2i00
χ4122-2-22-2-222-22-2-220000222-2-2-200000000002i−2i00000022-2-22i−2i−2i2i0000000000002i−2i00000000
χ4222-2-22-2-222-22-2-220000222-2-2-200000000002i−2i000000-2-222−2i2i2i−2i0000000000002i−2i00000000
χ4322-2-22-2-222-22-2-220000222-2-2-20000000000−2i2i00000022-2-2−2i2i2i−2i000000000000−2i2i00000000
χ4422-2-22-2-222-22-2-220000222-2-2-20000000000−2i2i000000-2-2222i−2i−2i2i000000000000−2i2i00000000
χ4544444-4-4-4-44-2-2-2-20000-222-222000000004-400000000000000000000-220000000000000000
χ4644444-4-4-4-44-2-2-2-20000-222-22200000000-44000000000000000000002-20000000000000000
χ474444-44-44-4-4-2-2-2-200002-222-220000040-4000000000000000000000-2000200000000000000
χ484444-44-44-4-4-2-2-2-200002-222-2200000-4040000000000000000000002000-200000000000000
χ494444-4-44-44-4-2-2-2-2000022-222-2000040-4000000000000000000000-20002000000000000000
χ504444-4-44-44-4-2-2-2-2000022-222-20000-4040000000000000000000002000-2000000000000000
χ5144-4-4444-4-4-4-222-244-4-4-2222-2-2000000000000-2-22200000000000000000000000000000000
χ5244-4-4444-4-4-4-222-2-4-444-2222-2-200000000000022-2-200000000000000000000000000000000
χ5344-4-44-4-444-4-222-20000-2-2-222200000000004i−4i00000000000000000000000000−2i2i00000000
χ5444-4-44-4-444-4-222-20000-2-2-22220000000000−4i4i000000000000000000000000002i−2i00000000
χ5544-4-4-44-4-4444-4-440000-4-4444-4000000000000000000000000000000000000000000000000
χ5644-4-4-44-4-444-222-2000022-2-2-22000000000000000000000000000000000000−2i32i30000000000
χ5744-4-4-44-4-444-222-2000022-2-2-220000000000000000000000000000000000002i3−2i30000000000
χ5844-4-4-4-444-444-4-440000-44-44-44000000000000000000000000000000000000000000000000
χ5944-4-4-4-444-44-222-200002-22-22-20000000000000000000000000000000000−2i32i3000000000000
χ6044-4-4-4-444-44-222-200002-22-22-200000000000000000000000000000000002i3−2i3000000000000
χ614-44-400000044-4-42-22-2000000004-4000000002-22-2002-22-200000000000000000000000000
χ624-44-400000044-4-42-22-200000000-44000000002-22-200-22-2200000000000000000000000000
χ634-44-400000044-4-4-22-22000000004-400000000-22-2200-22-2200000000000000000000000000
χ644-44-400000044-4-4-22-2200000000-4400000000-22-22002-22-200000000000000000000000000
χ654-4-440000004-44-42-2-220000004-400000000002-2-22002-2-2200000000000000000000000000
χ664-4-440000004-44-42-2-22000000-4400000000002-2-2200-222-200000000000000000000000000
χ674-4-440000004-44-4-222-20000004-40000000000-222-200-222-200000000000000000000000000
χ684-4-440000004-44-4-222-2000000-440000000000-222-2002-2-2200000000000000000000000000
χ698-88-8000000-4-4444-44-4000000000000000000-22-2200000000000000000000000000000000
χ708-88-8000000-4-444-44-440000000000000000002-22-200000000000000000000000000000000
χ718-8-88000000-44-444-4-44000000000000000000-222-200000000000000000000000000000000
χ728-8-88000000-44-44-444-40000000000000000002-2-2200000000000000000000000000000000

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