Finite Group Databasebeta

← Group #10768705

Character table — Group #10768705

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222224444666688888888888888881212161616161616161616161616161624242424242424242424242448
order1222223666446622442224444444668812122466812121212121212242424242244444444888
χ1111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-111-1-1111111-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111-1-11-1-111-1-1-1-11111111-1-1-11-111-1-111-1-11-11-1-1-111-1-111-1
χ41111111111111111111-1-11-1-1-1-111-1-1-1-111111-11-11-1-1-111-1-1111-11-1-1-1-1-111-1-11
χ5111111111111111111-11-1-11-111-1-1-1-1-1-11111-111-1-1111-1-1-1-111-1-1-11-1111-1-1-1-11
χ6111111111111111111-11-1-11-1-1-111-1-1111111-11-1-1-11-1-11111-1-1-1-1-11-11-1-11111-1
χ7111111111111111111-1-11-1-11111111-1-11111-1-1-11-1-11111-1-1-1-1-11-1-11-11111-1-1-1
χ8111111111111111111-1-11-1-11-1-1-1-111111111-1-111-1-1-1-1-1-11111-11-1-11-1-1-1-1-1111
χ911111111111111-1-1-1-11111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111-1-1-1-1111111-1-1-1-111-1-111-1-111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ1111111111111111-1-1-1-11-1-11-1-111-1-1-1-11111-1-11-1-1-11-111-1-111-1-1-11-1111-1-111-1-11
χ1211111111111111-1-1-1-11-1-11-1-1-1-111-1-1-1-111-1-11-11-11-1-1-111-1-111-11-111111-1-111-1
χ1311111111111111-1-1-1-1-11-1-11-111-1-1-1-1-1-111-1-1-111-1-1111-1-1-1-111111-11-1-1-11111-1
χ1411111111111111-1-1-1-1-11-1-11-1-1-111-1-11111-1-1-11-1-1-11-1-11111-1-1111-11-111-1-1-1-11
χ1511111111111111-1-1-1-1-1-11-1-11111111-1-111-1-1-1-1-11-1-11111-1-1-1-11-111-11-1-1-1-1111
χ1611111111111111-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111-111-111111-1-1-1
χ172222222222-2-22222-2-200200-200002200-2-22-2000-200000000000-200200000000
χ182222222222-2-22222-2-200-20020000-2-200-2-22-2000200000000000200-200000000
χ192222222222-2-222-2-22200200-200002200-2-2-22000-200000000000200-200000000
χ202222222222-2-222-2-22200-20020000-2-200-2-2-22000200000000000-200200000000
χ21222222-1-1-1-122-1-100002222222222-1-122-1-100-1-12-1-1-1-1-1-1-1-1-1-1-10000000000000
χ22222222-1-1-1-122-1-10000222222-2-2-2-2-1-1-2-2-1-100-1-1-2-1-1-1111111110000000000000
χ23222222-1-1-1-122-1-100002-2-22-2-222-2-21122-1-100-11-21-11-1-111-1-1110000000000000
χ24222222-1-1-1-122-1-100002-2-22-2-2-2-22211-2-2-1-100-1121-1111-1-111-1-10000000000000
χ25222222-1-1-1-122-1-10000-22-2-22-222-2-211-2-2-1-1001-1211-1-1-11111-1-10000000000000
χ26222222-1-1-1-122-1-10000-22-2-22-2-2-2221122-1-1001-1-211-111-1-1-1-1110000000000000
χ27222222-1-1-1-122-1-10000-2-22-2-222222-1-1-2-2-1-10011-2-111-1-1-1-111110000000000000
χ28222222-1-1-1-122-1-10000-2-22-2-22-2-2-2-2-1-122-1-100112-1111111-1-1-1-10000000000000
χ292222-2-222222-2-2-22222200-200000000002-2-2-22000-200000000020-20000000000
χ302222-2-222222-2-2-22222-200200000000002-2-2-2-20002000000000-2020000000000
χ312222-2-222222-2-2-2-2-2-2-2200-200000000002-2222000-2000000000-2020000000000
χ322222-2-222222-2-2-2-2-2-2-2-200200000000002-222-2000200000000020-20000000000
χ332222-2-22222-22-2-222-2-20200-2000000000-22-2202000-20000000000020-20000000
χ342222-2-22222-22-2-222-2-20-2002000000000-22-220-2000200000000000-2020000000
χ352222-2-22222-22-2-2-2-2220200-2000000000-222-202000-200000000000-2020000000
χ362222-2-22222-22-2-2-2-2220-2002000000000-222-20-200020000000000020-20000000
χ37444444-2-2-2-2-4-4-2-2000000400-40000-2-2002200000200000000000000000000000
χ38444444-2-2-2-2-4-4-2-2000000-4004000022002200000-200000000000000000000000
χ394444-4-4-2-2-2-24-4220000400-40000000000-2200-200020000000000000000000000
χ404444-4-4-2-2-2-24-4220000-40040000000000-22002000-20000000000000000000000
χ414444-4-4-2-2-2-2-442200000400-40000000002-2000-20002000000000000000000000
χ424444-4-4-2-2-2-2-442200000-40040000000002-20002000-2000000000000000000000
χ4344-4-44-44-44-400-440000000000000000000000000000000000000000000000−2i22i20
χ4444-4-44-44-44-400-4400000000000000000000000000000000000000000000002i2−2i20
χ4544-4-4-444-44-4004-40000000000000000−2i22i200000000000000−2i22i2000000000000000
χ4644-4-4-444-44-4004-400000000000000002i2−2i2000000000000002i2−2i2000000000000000
χ4744-4-4-44-22-2200-2200000000000000−2i32i3−2i22i200000000000000i2−i26−60000000000000
χ4844-4-4-44-22-2200-2200000000000000−2i32i32i2−2i200000000000000−i2i2−660000000000000
χ4944-4-4-44-22-2200-22000000000000002i3−2i3−2i22i200000000000000i2−i2−660000000000000
χ5044-4-4-44-22-2200-22000000000000002i3−2i32i2−2i200000000000000−i2i26−60000000000000
χ514-44-40044-4-400004-400000000002i−2i00000000000000002i−2i0000000000002i−2i000
χ524-44-40044-4-400004-40000000000−2i2i0000000000000000−2i2i000000000000−2i2i000
χ534-44-40044-4-40000-4400000000002i−2i00000000000000002i−2i000000000000−2i2i000
χ544-44-40044-4-40000-440000000000−2i2i0000000000000000−2i2i0000000000002i−2i000
χ554-4-44004-4-440000004-40000002-200000000000000002-20000000000002-200000
χ564-4-44004-4-440000004-4000000-220000000000000000-22000000000000-2200000
χ574-4-44004-4-44000000-440000002-200000000000000002-2000000000000-2200000
χ584-4-44004-4-44000000-44000000-220000000000000000-220000000000002-200000
χ5988-8-88-8-44-44004-40000000000000000000000000000000000000000000000000
χ608-88-800-4-44400000000000000004i−4i0000000000000000−2i2i00000000000000000
χ618-88-800-4-4440000000000000000−4i4i00000000000000002i−2i00000000000000000
χ628-8-8800-444-4000000000000004-40000000000000000-220000000000000000000
χ638-8-8800-444-400000000000000-4400000000000000002-20000000000000000000

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