Finite Group Databasebeta

← Group #10826852

Character table — Group #10826852

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222224444444444444466668888888888888888888888121212121212161616161616161624242424242424244848
order1222223444466644444444661212121244442244446666121212121212121212121212224444881212242424242222444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-1111111111111-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111
χ7111111111111111111-1-1-1-1111111-1-1-1-111-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1111111-1-1
χ911111111111111-1-1-1-1111111111111111-1-1-11-111-1-1-1-1-1-111-1-111111111111-1-1-111-1-1-1-1-1-111-1-11-1
χ1011111111111111-1-1-1-111111111111111-11-1-1-11-1-111-1-1-1-1-1-1111111111111-11-1-1-1-111-1-1-1-1-1-111-11
χ1111111111111111-1-1-1-11111111111-1-1-1-11-1-1-11-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-111-1-11111-1-111-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-11-1-1-11-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1-1-111111111-1-11-1
χ1311111111111111-1-1-1-1-1-1-1-111111111111-1111-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1111-1-111-1-11111-1-1-11
χ1411111111111111-1-1-1-1-1-1-1-11111111111-1111-11-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11-11111-1-1-1-111-1-1111-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-1-1111-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-11-1-111-1-1-1-1-1-111-1-1-1-1-1-111111-11111-1-111-1-111-1-1-11
χ172222222-2-2-2-222222-2-2000022-2-2-2-22222000000000022-2-200000000-2-20000000000002-200000000
χ182222222-2-2-2-222222-2-2000022-2-2-2-2-2-2-2-2000000000022-2-20000000022000000000000-2200000000
χ192222222-2-2-2-2222-2-222000022-2-2-2-222220000000000-2-22200000000-2-2000000000000-2200000000
χ202222222-2-2-2-2222-2-222000022-2-2-2-2-2-2-2-20000000000-2-22200000000220000000000002-200000000
χ21222222-12222-1-1-122222222-1-1-1-1-1-10000222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-10000000000
χ22222222-12222-1-1-122222222-1-1-1-1-1-10000-2-222-2-21111-1-1-1-11111-1-1-1-1000000-2-2-1-111110000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1000022-2-222-1-1-1-1-1-1-1-1-1-1-1-11111000000-2-21111110000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-10000-2-2-2-2-2-21111-1-1-1-1111111110000002211-1-1-1-10000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-100002-2-2-22-2-1-1111111-1-111-1-1-1-10000002-211-1-1110000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-10000-22-2-2-2211-1-1111111-1-1-1-1-1-1000000-221111-1-10000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100002-2222-2-1-1111111-1-1111111000000-22-1-111-1-10000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-10000-2222-2211-1-1111111-1-111110000002-2-1-1-1-1110000000000
χ292222-2-222-22-222200000000-2-22-22-222-2-202000-20022000000-2-200002-20000000000000000002-200
χ302222-2-222-22-222200000000-2-22-22-222-2-20-2000200-2-20000002200002-2000000000000000000-2200
χ312222-2-222-22-222200000000-2-22-22-2-2-22202000-20022000000-2-20000-22000000000000000000-2200
χ322222-2-222-22-222200000000-2-22-22-2-2-2220-2000200-2-2000000220000-220000000000000000002-200
χ332222-2-22-22-2222200000000-2-2-22-2222-2-22000-2022000000-2-2000000-2200000000000000002-20000
χ342222-2-22-22-2222200000000-2-2-22-2222-2-2-200020-2-200000022000000-220000000000000000-220000
χ352222-2-22-22-2222200000000-2-2-22-22-2-2222000-2022000000-2-20000002-20000000000000000-220000
χ362222-2-22-22-2222200000000-2-2-22-22-2-222-200020-2-2000000220000002-200000000000000002-20000
χ372-2-22-22222-2-2-2-222-22-222-2-2-22-2-2220000002-20000002-22-2000022-2-2000000002-200000000000000
χ382-2-22-22222-2-2-2-222-22-2-2-222-22-2-222000000-220000002-22-20000-2-22200000000-2200000000000000
χ392-2-22-22222-2-2-2-22-22-2222-2-2-22-2-222000000-22000000-22-22000022-2-200000000-2200000000000000
χ402-2-22-22222-2-2-2-22-22-22-2-222-22-2-2220000002-2000000-22-220000-2-222000000002-200000000000000
χ412-2-22-222-2-222-2-222-2-220000-2222-2-2000000000000002-2-22000000000022-2-200000000002-2000000
χ422-2-22-222-2-222-2-222-2-220000-2222-2-2000000000000002-2-220000000000-2-2220000000000-22000000
χ432-2-22-222-2-222-2-22-222-20000-2222-2-200000000000000-222-2000000000022-2-20000000000-22000000
χ442-2-22-222-2-222-2-22-222-20000-2222-2-200000000000000-222-20000000000-2-22200000000002-2000000
χ452-2-22-22-122-2-211-12-22-222-2-21-111-1-10000002-200−i3i3−i3i3-11-11−i3i3−i3i3-1-11100000000-11−i3i3−i3i30000000000
χ462-2-22-22-122-2-211-12-22-222-2-21-111-1-10000002-200i3−i3i3−i3-11-11i3−i3i3−i3-1-11100000000-11i3−i3i3−i30000000000
χ472-2-22-22-122-2-211-12-22-2-2-2221-111-1-1000000-2200−i3i3−i3i3-11-11−i3i3−i3i311-1-1000000001-1i3−i3i3−i30000000000
χ482-2-22-22-122-2-211-12-22-2-2-2221-111-1-1000000-2200i3−i3i3−i3-11-11i3−i3i3−i311-1-1000000001-1−i3i3−i3i30000000000
χ492-2-22-22-122-2-211-1-22-2222-2-21-111-1-1000000-2200−i3i3i3−i31-11-1−i3i3i3−i3-1-111000000001-1−i3i3i3−i30000000000
χ502-2-22-22-122-2-211-1-22-2222-2-21-111-1-1000000-2200i3−i3−i3i31-11-1i3−i3−i3i3-1-111000000001-1i3−i3−i3i30000000000
χ512-2-22-22-122-2-211-1-22-22-2-2221-111-1-10000002-200−i3i3i3−i31-11-1−i3i3i3−i311-1-100000000-11i3−i3−i3i30000000000
χ522-2-22-22-122-2-211-1-22-22-2-2221-111-1-10000002-200i3−i3−i3i31-11-1i3−i3−i3i311-1-100000000-11−i3i3i3−i30000000000
χ53444444-2-4-4-4-4-2-2-244-4-40000-2-2222200000000000000-2-22200000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-4440000-2-222220000000000000022-2-200000000000000000000000000000000
χ554444-4-4-24-44-4-2-2-20000000022-22-22000004000-400-2-2000000220000000000000000000000000000
χ564444-4-4-24-44-4-2-2-20000000022-22-2200000-400040022000000-2-20000000000000000000000000000
χ574444-4-4-2-44-44-2-2-200000000222-22-200004000-40-2-200000022000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-200000000222-22-20000-40004022000000-2-2000000000000000000000000000000
χ5944-4-400400004-4-400002-22-2000000004i−4i0000000000000000002-22-2002i−2i2i−2i000000000000000000
χ6044-4-400400004-4-400002-22-200000000−4i4i0000000000000000002-22-200−2i2i−2i2i000000000000000000
χ6144-4-400400004-4-40000-22-22000000004i−4i000000000000000000-22-2200−2i2i−2i2i000000000000000000
χ6244-4-400400004-4-40000-22-2200000000−4i4i000000000000000000-22-22002i−2i2i−2i000000000000000000
χ634-44-40040000-44-400002-2-220000004i−4i000000000000000000002-2-22002i−2i−2i2i000000000000000000
χ644-44-40040000-44-400002-2-22000000−4i4i000000000000000000002-2-2200−2i2i2i−2i000000000000000000
χ654-44-40040000-44-40000-222-20000004i−4i00000000000000000000-222-200−2i2i2i−2i000000000000000000
χ664-44-40040000-44-40000-222-2000000−4i4i00000000000000000000-222-2002i−2i−2i2i000000000000000000
χ674-4-444-444-4-44-4-44000000004-4-444-400000000000000000000000000000000000000000000000000
χ684-4-444-44-444-4-4-44000000004-44-4-4400000000000000000000000000000000000000000000000000
χ694-4-444-4-24-4-4422-200000000-222-2-22000000000000−2i32i30000002i3−2i30000000000000000000000000000
χ704-4-444-4-24-4-4422-200000000-222-2-220000000000002i3−2i3000000−2i32i30000000000000000000000000000
χ714-4-444-4-2-444-422-200000000-22-222-20000000000−2i32i30000002i3−2i3000000000000000000000000000000
χ724-4-444-4-2-444-422-200000000-22-222-200000000002i3−2i3000000−2i32i3000000000000000000000000000000
χ734-4-44-44-2-4-44422-24-4-4400002-2-2-22200000000000000-222-200000000000000000000000000000000
χ744-4-44-44-2-4-44422-2-444-400002-2-2-222000000000000002-2-2200000000000000000000000000000000
χ7588-8-800-40000-44400004-44-40000000000000000000000000000-22-22000000000000000000000000
χ7688-8-800-40000-4440000-44-4400000000000000000000000000002-22-2000000000000000000000000
χ778-88-800-400004-4400004-4-440000000000000000000000000000-222-2000000000000000000000000
χ788-88-800-400004-440000-444-400000000000000000000000000002-2-22000000000000000000000000

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