Finite Group Databasebeta

← Group #10827245

Character table — Group #10827245

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222223444466622446666661212121222222444666666661212444468812121224242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1111-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1111111-1-1111111-1-1
χ911111111111111-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-1-11111-1-11-1
χ1011111111111111-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-11111-1-1-1-111-11
χ1111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1111-1-1-11111-1-1-1-111-1-1-11
χ1211111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11111-1-1111-1
χ1311111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111111-11-1-11-1-111-1-1-1-111-1-111-11
χ1411111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-11-1-1111111-1-111-1-11-1
χ1511111111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-11111-11-111-111-1-111-1-1-1-1-1-1111-1
χ1611111111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-11-111-111-1-1-1-1111111-1-1-11
χ172222222-2-2-2-222222-2-2222222-2-2-2-20000000000000000-2-222-2-20000000000002-200000000
χ182222222-2-2-2-222222-2-2222222-2-2-2-20000000000000000-2-2-2-222000000000000-2200000000
χ192222222-2-2-2-2222-2-22222-2-2-2-2-2-2-2-200000000000000002222-2-2000000000000-2200000000
χ202222222-2-2-2-2222-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-2220000000000002-200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-122-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-100001-2-21111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-10000-1-2-2-1-1-11111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-10000122111-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-11111-1-1-1-122-2-222-2-2-1-1-1-11111110000-12-211-1-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-11111-1-1-1-122-2-2-2-222-1-1-1-111111100001-22-1-1111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-11111-1-1-1-1-2-22222-2-21111-1-1-1-1110000-1-2211-111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-11111-1-1-1-1-2-222-2-2221111-1-1-1-111000012-2-1-11-1-111000000000000
χ292222-2-2222-2-22222-22-2-2-222-2-2-2-22200002-22-2000000002-200002002-2-20000000000000000
χ302222-2-2222-2-22222-22-2-2-222-2-2-2-2220000-22-22000000002-20000-200-2220000000000000000
χ312222-2-2222-2-2222-22-22-2-2-2-222-2-22200002-2-2200000000-220000200-22-20000000000000000
χ322222-2-2222-2-2222-22-22-2-2-2-222-2-2220000-222-200000000-220000-2002-220000000000000000
χ332222-2-22-2-2222222-2-22-2-222-2-222-2-20000000000000000-22000000000000002-2002-2000000
χ342222-2-22-2-2222222-2-22-2-222-2-222-2-20000000000000000-2200000000000000-2200-22000000
χ352222-2-22-2-222222-222-2-2-2-2-22222-2-200000000000000002-2000000000000002-200-22000000
χ362222-2-22-2-222222-222-2-2-2-2-22222-2-200000000000000002-200000000000000-22002-2000000
χ372222-2-2-122-2-2-1-1-12-22-211-1-11111-1-100002-22-2−i3−i3i3i3−i3−i3i3i3-110000-100-111−i3i3−i3i3000000000000
χ382222-2-2-122-2-2-1-1-12-22-211-1-11111-1-100002-22-2i3i3−i3−i3i3i3−i3−i3-110000-100-111i3−i3i3−i3000000000000
χ392222-2-2-122-2-2-1-1-12-22-211-1-11111-1-10000-22-22−i3−i3i3i3−i3−i3i3i3-1100001001-1-1i3−i3i3−i3000000000000
χ402222-2-2-122-2-2-1-1-12-22-211-1-11111-1-10000-22-22i3i3−i3−i3i3i3−i3−i3-1100001001-1-1−i3i3−i3i3000000000000
χ412222-2-2-122-2-2-1-1-1-22-221111-1-111-1-100002-2-22−i3−i3i3i3i3i3−i3−i31-10000-1001-11−i3i3i3−i3000000000000
χ422222-2-2-122-2-2-1-1-1-22-221111-1-111-1-100002-2-22i3i3−i3−i3−i3−i3i3i31-10000-1001-11i3−i3−i3i3000000000000
χ432222-2-2-122-2-2-1-1-1-22-221111-1-111-1-10000-222-2−i3−i3i3i3i3i3−i3−i31-10000100-11-1i3−i3−i3i3000000000000
χ442222-2-2-122-2-2-1-1-1-22-221111-1-111-1-10000-222-2i3i3−i3−i3−i3−i3i3i31-10000100-11-1−i3i3i3−i3000000000000
χ4522-2-22-222-22-2-2-2200002-200002-22-2002-2000000002-22-2002i−2i2i−2i0000000000000000002i−2i00
χ4622-2-22-222-22-2-2-2200002-200002-22-2002-2000000002-22-200−2i2i−2i2i000000000000000000−2i2i00
χ4722-2-22-222-22-2-2-2200002-200002-22-200-2200000000-22-22002i−2i2i−2i000000000000000000−2i2i00
χ4822-2-22-222-22-2-2-2200002-200002-22-200-2200000000-22-2200−2i2i−2i2i0000000000000000002i−2i00
χ4922-2-22-22-22-22-2-2200002-20000-22-222-20000002-22-20000002i−2i−2i2i00000000000000002i−2i0000
χ5022-2-22-22-22-22-2-2200002-20000-22-222-20000002-22-2000000−2i2i2i−2i0000000000000000−2i2i0000
χ5122-2-22-22-22-22-2-2200002-20000-22-22-22000000-22-220000002i−2i−2i2i0000000000000000−2i2i0000
χ5222-2-22-22-22-22-2-2200002-20000-22-22-22000000-22-22000000−2i2i2i−2i00000000000000002i−2i0000
χ53444444-2-4-4-4-4-2-2-244-4-4-2-2-2-2-2-2222200000000000000002200000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-2222222220000000000000000-2-200000000000000000000000000
χ554444-4-4-2-4-444-2-2-24-4-4422-2-222-2-22200000000000000002-200000000000000000000000000
χ564444-4-4-2-4-444-2-2-2-444-42222-2-2-2-2220000000000000000-2200000000000000000000000000
χ5744-4-44-4-24-44-422-20000-220000-22-22004-400000000-22-220000000000000000000000000000
χ5844-4-44-4-24-44-422-20000-220000-22-2200-44000000002-22-20000000000000000000000000000
χ5944-4-44-4-2-44-4422-20000-2200002-22-24-4000000-22-2200000000000000000000000000000000
χ6044-4-44-4-2-44-4422-20000-2200002-22-2-440000002-22-200000000000000000000000000000000
χ6144-4-4-4444-4-44-4-440000-440000-444-400000000000000000000000000000000000000000000
χ6244-4-4-444-444-4-4-440000-4400004-4-4400000000000000000000000000000000000000000000
χ6344-4-4-44-24-4-4422-200002-200002-2-22000000000000−2i32i32i3−2i30000000000000000000000000000
χ6444-4-4-44-24-4-4422-200002-200002-2-220000000000002i3−2i3−2i32i30000000000000000000000000000
χ6544-4-4-44-2-444-422-200002-20000-222-200000000−2i32i32i3−2i300000000000000000000000000000000
χ6644-4-4-44-2-444-422-200002-20000-222-2000000002i3−2i3−2i32i300000000000000000000000000000000
χ678-88-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ688-88-800-40000-444000000−4i34i300000000000000000000000000000000000000000000000000
χ698-88-800-40000-4440000004i3−4i300000000000000000000000000000000000000000000000000
χ708-8-880080000-88-80000000000000000000000000000000000000000000000000000000000
χ718-8-8800-400004-4400000000−4i34i3000000000000000000000000000000000000000000000000
χ728-8-8800-400004-44000000004i3−4i3000000000000000000000000000000000000000000000000

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