Finite Group Databasebeta

← Group #10830415

Character table — Group #10830415

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order1222223444466622226612121212222244446666666612121212121212124444668824242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1
χ911111111111111-1-1-1-11111111-1111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111-111-1-11-1-1-11-111-1-11-1
χ1011111111111111-1-1-1-11111111-1111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-111-1-1-1111-11-1-111-11
χ1111111111111111-1-1-1-11111111-1-1-11-111-1-1-1-111-1-111-1-111111111-1-1-11-1-1111-1-1-11-1-1-111-11
χ1211111111111111-1-1-1-11111111-1-1-11-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11-1-111-1111-1111-1-11-1
χ1311111111111111-1-1-1-1111111-1111-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-11-1-111-11-1-1-1111-1-1-11
χ1411111111111111-1-1-1-1111111-1111-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-11-1-1111-1111-1-1-1111-1
χ1511111111111111-1-1-1-1111111-11-1-1-1111-1-1-1-1-1-111-1-11111111111-1-11-111-1-1-11-1-1-11-1-1111-1
χ1611111111111111-1-1-1-1111111-11-1-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-111-1-11-1111-111-1-1-11
χ172222222-2-2-2-222222-2-222-2-2-2-20000000022-2-200000000000022-2-200000000002-200000000
χ182222222-2-2-2-222222-2-222-2-2-2-20000000022-2-2000000000000-2-2220000000000-2200000000
χ192222222-2-2-2-2222-2-22222-2-2-2-200000000-2-22200000000000022-2-20000000000-2200000000
χ202222222-2-2-2-2222-2-22222-2-2-2-200000000-2-222000000000000-2-22200000000002-200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-11111000011-2-21111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-2-222-2-222-1-1-1-111111111-1-1-1-10000-1-1-2-21111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111100001122-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-12-2222-2-2-21111-1-111-1-11111110000-1-12-2-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-12-2-2-22-2221111-1-111-1-111-1-1-1-1000011-2211-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2222-22-2-2111111-1-111-1-111110000-1-1-2211-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-22-2-2-2222111111-1-111-1-1-1-1-1-10000112-2-1-111000000000000
χ292222-2-222-22-22220000-2-22-22-202000-2000000002200-2-200002-22-20000000002000-2000000
χ302222-2-222-22-22220000-2-22-22-202000-2000000002200-2-20000-22-22000000000-20002000000
χ312222-2-222-22-22220000-2-22-22-20-2000200000000-2-2002200002-22-2000000000-20002000000
χ322222-2-222-22-22220000-2-22-22-20-2000200000000-2-200220000-22-220000000002000-2000000
χ332222-2-22-22-222220000-2-2-22-222000-200000002200-2-20000002-2-22000000002000-20000000
χ342222-2-22-22-222220000-2-2-22-222000-200000002200-2-2000000-222-200000000-200020000000
χ352222-2-22-22-222220000-2-2-22-22-200020000000-2-200220000002-2-2200000000-200020000000
χ362222-2-22-22-222220000-2-2-22-22-200020000000-2-20022000000-222-2000000002000-20000000
χ3722-2-22-2222-2-2-2-222-22-2-2222-2-2000000002-22-20000000000000000000000000000002i−2i2i−2i00
χ3822-2-22-2222-2-2-2-222-22-2-2222-2-2000000002-22-2000000000000000000000000000000−2i2i−2i2i00
χ3922-2-22-2222-2-2-2-22-22-22-2222-2-200000000-22-220000000000000000000000000000002i−2i−2i2i00
χ4022-2-22-2222-2-2-2-22-22-22-2222-2-200000000-22-22000000000000000000000000000000−2i2i2i−2i00
χ4122-2-22-22-2-222-2-222-2-22-22-2-222002-2002-22-2-220000000022-2-200002-2000000000000000000
χ4222-2-22-22-2-222-2-222-2-22-22-2-22200-2200-222-2-2200000000-2-2220000-22000000000000000000
χ4322-2-22-22-2-222-2-22-222-2-22-2-222002-200-22-222-200000000-2-22200002-2000000000000000000
χ4422-2-22-22-2-222-2-22-222-2-22-2-22200-22002-2-222-20000000022-2-20000-22000000000000000000
χ4522-2-22-2-1-2-22211-12-2-221-111-1-1002-2002-2-111-1−i3i3−i3i3−i3i3−i3i3-1-1110000-1100−i3i3−i3i3000000000000
χ4622-2-22-2-1-2-22211-12-2-221-111-1-1002-2002-2-111-1i3−i3i3−i3i3−i3i3−i3-1-1110000-1100i3−i3i3−i3000000000000
χ4722-2-22-2-1-2-22211-12-2-221-111-1-100-2200-22-111-1−i3i3−i3i3−i3i3−i3i311-1-100001-100i3−i3i3−i3000000000000
χ4822-2-22-2-1-2-22211-12-2-221-111-1-100-2200-22-111-1i3−i3i3−i3i3−i3i3−i311-1-100001-100−i3i3−i3i3000000000000
χ4922-2-22-2-1-2-22211-1-222-21-111-1-1002-200-221-1-11−i3i3i3−i3−i3i3i3−i311-1-10000-1100−i3i3i3−i3000000000000
χ5022-2-22-2-1-2-22211-1-222-21-111-1-1002-200-221-1-11i3−i3−i3i3i3−i3−i3i311-1-10000-1100i3−i3−i3i3000000000000
χ5122-2-22-2-1-2-22211-1-222-21-111-1-100-22002-21-1-11−i3i3i3−i3−i3i3i3−i3-1-11100001-100i3−i3−i3i3000000000000
χ5222-2-22-2-1-2-22211-1-222-21-111-1-100-22002-21-1-11i3−i3−i3i3i3−i3−i3i3-1-11100001-100−i3i3i3−i3000000000000
χ53444444-2-4-4-4-4-2-2-244-4-4-2-2222200000000-2-222000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-222220000000022-2-2000000000000000000000000000000000000
χ554444-4-4-24-44-4-2-2-2000022-22-2204000-400000000-2-200220000000000000000000000000000
χ564444-4-4-24-44-4-2-2-2000022-22-220-40004000000002200-2-20000000000000000000000000000
χ574444-4-4-2-44-44-2-2-20000222-22-24000-40000000-2-20022000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-20000222-22-2-4000400000002200-2-2000000000000000000000000000000
χ5944-4-44-4-244-4-422-24-44-42-2-2-22200000000-22-22000000000000000000000000000000000000
χ6044-4-44-4-244-4-422-2-44-442-2-2-222000000002-22-2000000000000000000000000000000000000
χ6144-4-4-4444-4-44-4-4400004-44-4-44000000000000000000000000000000000000000000000000
χ6244-4-4-444-444-4-4-4400004-4-444-4000000000000000000000000000000000000000000000000
χ6344-4-4-44-24-4-4422-20000-22-222-2000000000000−2i32i3002i3−2i3000000000000000000000000000000
χ6444-4-4-44-24-4-4422-20000-22-222-20000000000002i3−2i300−2i32i3000000000000000000000000000000
χ6544-4-4-44-2-444-422-20000-222-2-2200000000000000−2i32i3002i3−2i30000000000000000000000000000
χ6644-4-4-44-2-444-422-20000-222-2-22000000000000002i3−2i300−2i32i30000000000000000000000000000
χ678-88-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ688-88-800-40000-444000000000000000000000000000000−2i32i3−2i32i3000000000000000000000000
χ698-88-800-40000-4440000000000000000000000000000002i3−2i32i3−2i3000000000000000000000000
χ708-8-880080000-88-80000000000000000000000000000000000000000000000000000000000
χ718-8-8800-400004-44000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ728-8-8800-400004-440000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000

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