Finite Group Databasebeta

← Group #10843149

Character table — Group #10843149

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222244444444448888888888888888888888888812121212121212121616161616161624242424242424244848
order1222223444466622446612121212222224446666666688121212121212121244448888668242424244444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-111111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1111-1-1
χ4111111111111111111111111111-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-111-1-1-111
χ5111111111111111111111111-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-111-1-111111-1-1-1-1-1
χ6111111111111111111111111-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-111111
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11-1-111-111-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11-1-1111-1-111111-1-1
χ911111111111111-1-1-1-111111111-111-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-11-1-11-111-1-11
χ1011111111111111-1-1-1-111111111-111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-11-1-111-1
χ1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1111-11-1
χ1211111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-11-11
χ1311111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111-1-1111-1-11-1-1-111-1
χ1411111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111-1-111-111-1111-1-11
χ1511111111111111-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-11111-1-111111111111111-1-1-111-1-1-1-1-1-11-1-11-11
χ1611111111111111-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-11-1
χ17222222-12222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-1-12-1-1-1-10000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1222-2-22-2-2-1-1-1-1-1-1-1-1-2-2-1-1-1-111110000000011-211110000000000
χ19222222-12222-1-1-12222-1-1-1-1-1-1-2-2-222-2-2-2-1-111111122-1-111111100000000-1-1-2-1-1110000000000
χ20222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-222-1-1111111-2-2-1-111-1-1-1-10000000011211-1-10000000000
χ21222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-222-22211-1-1-1-111-2-21111-1-1-1-100000000-1-1-211110000000000
χ22222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-2-2-2-2-2-211-1-1-1-111221111111100000000112-1-1-1-10000000000
χ23222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-2-2111111-1-1-2-211-1-1111100000000-1-1211-1-10000000000
χ24222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22-2-2222111111-1-12211-1-1-1-1-1-10000000011-2-1-1110000000000
χ252222-2-222-2-222220000-2-22-22-200200-200000000220000-2-2000022-2-200-2-200000000000000200
χ262222-2-222-2-222220000-2-22-22-200200-200000000220000-2-20000-2-222002200000000000000-200
χ272222-2-222-2-222220000-2-22-22-200-200200000000-2-2000022000022-2-2002200000000000000-200
χ282222-2-222-2-222220000-2-22-22-200-200200000000-2-20000220000-2-22200-2-200000000000000200
χ292222-2-22-222-222222-2-2-2-2-22-22000000002200000000-2-2000000000022000000000-2002-200000
χ302222-2-22-222-222222-2-2-2-2-22-22000000002200000000-2-20000000000-2-2000000000200-2200000
χ312222-2-22-222-2222-2-222-2-2-22-2200000000-2-20000000022000000000022000000000200-2-200000
χ322222-2-22-222-2222-2-222-2-2-22-2200000000-2-200000000220000000000-2-2000000000-2002200000
χ332-22-22-222-22-2-2-222-22-22-22-2-22000000002-2000000002-20000002i−2i2i−2i0000000000002i−2i0000000
χ342-22-22-222-22-2-2-222-22-22-22-2-22000000002-2000000002-2000000−2i2i−2i2i000000000000−2i2i0000000
χ352-22-22-222-22-2-2-22-22-222-22-2-2200000000-2200000000-220000002i−2i2i−2i000000000000−2i2i0000000
χ362-22-22-222-22-2-2-22-22-222-22-2-2200000000-2200000000-22000000−2i2i−2i2i0000000000002i−2i0000000
χ372-22-2-22222-2-2-2-220000-2222-2-22-20000000022-2-20000000000002i−2i−2i2i00000000000000002i−2i000
χ382-22-2-22222-2-2-2-220000-2222-2-22-20000000022-2-2000000000000−2i2i2i−2i0000000000000000−2i2i000
χ392-22-2-22222-2-2-2-220000-2222-2-2-2200000000-2-2220000000000002i−2i−2i2i0000000000000000−2i2i000
χ402-22-2-22222-2-2-2-220000-2222-2-2-2200000000-2-222000000000000−2i2i2i−2i00000000000000002i−2i000
χ412-22-2-222-2-222-2-222-2-22-22-2-2220002-20002-20000002-2-22000000000000002-202-2000000000000
χ422-22-2-222-2-222-2-222-2-22-22-2-222000-220002-2000000-22-2200000000000000-220-22000000000000
χ432-22-2-222-2-222-2-22-222-2-22-2-2220002-2000-22000000-222-2000000000000002-20-22000000000000
χ442-22-2-222-2-222-2-22-222-2-22-2-222000-22000-220000002-22-200000000000000-2202-2000000000000
χ452-22-2-22-1-2-22211-12-2-221-111-1-10002-2000-11−i3i3−i3i3−i3i32-21-1−i3i3−i3−i3i3i300000000-110-11−i3i30000000000
χ462-22-2-22-1-2-22211-12-2-221-111-1-10002-2000-11i3−i3i3−i3i3−i32-21-1i3−i3i3i3−i3−i300000000-110-11i3−i30000000000
χ472-22-2-22-1-2-22211-12-2-221-111-1-1000-22000-11−i3i3−i3i3−i3i3-221-1−i3i3i3i3−i3−i3000000001-101-1i3−i30000000000
χ482-22-2-22-1-2-22211-12-2-221-111-1-1000-22000-11i3−i3i3−i3i3−i3-221-1i3−i3−i3−i3i3i3000000001-101-1−i3i30000000000
χ492-22-2-22-1-2-22211-1-222-21-111-1-10002-20001-1−i3i3−i3i3i3−i3-22-11i3−i3−i3−i3i3i300000000-1101-1i3−i30000000000
χ502-22-2-22-1-2-22211-1-222-21-111-1-10002-20001-1i3−i3i3−i3−i3i3-22-11−i3i3i3i3−i3−i300000000-1101-1−i3i30000000000
χ512-22-2-22-1-2-22211-1-222-21-111-1-1000-220001-1−i3i3−i3i3i3−i32-2-11i3−i3i3i3−i3−i3000000001-10-11−i3i30000000000
χ522-22-2-22-1-2-22211-1-222-21-111-1-1000-220001-1i3−i3i3−i3−i3i32-2-11−i3i3−i3−i3i3i3000000001-10-11i3−i30000000000
χ534444444-4-4-4-4444000044-4-4-4-4000000000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-222220000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-20000-2-2222200000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2000022-22-2200400-400000000-2-200002200000000000000000000000000000
χ574444-4-4-24-4-44-2-2-2000022-22-2200-400400000000220000-2-200000000000000000000000000000
χ584444-4-4-2-444-4-2-2-244-4-4222-22-200000000-2-200000000220000000000000000000000000000000
χ594444-4-4-2-444-4-2-2-2-4-444222-22-2000000002200000000-2-20000000000000000000000000000000
χ6044-4-400400004-4-400000000000000002-2000000000000002-22-20000−2i22i2−2i22i200000000000000000
χ6144-4-400400004-4-400000000000000002-2000000000000002-22-200002i2−2i22i2−2i200000000000000000
χ6244-4-400400004-4-40000000000000000-2200000000000000-22-220000−2i22i22i2−2i200000000000000000
χ6344-4-400400004-4-40000000000000000-2200000000000000-22-2200002i2−2i2−2i22i200000000000000000
χ644-44-44-44-44-44-4-4400004-4-444-4000000000000000000000000000000000000000000000000000
χ654-44-44-4-24-44-422-24-44-4-22-222-200000000-2200000000-220000000000000000000000000000000
χ664-44-44-4-24-44-422-2-44-44-22-222-2000000002-2000000002-20000000000000000000000000000000
χ674-44-44-4-2-44-4422-20000-222-2-2200000000000000−2i32i300002i3−2i300000000000000000000000000000
χ684-44-44-4-2-44-4422-20000-222-2-22000000000000002i3−2i30000−2i32i300000000000000000000000000000
χ694-44-4-44-244-4-422-200002-2-2-2224-400000000-2-2220000000000000000000000000000000000000
χ704-44-4-44-244-4-422-200002-2-2-222-440000000022-2-20000000000000000000000000000000000000
χ7188-8-800-40000-44400000000000000004-400000000000000-22-220000000000000000000000000
χ7288-8-800-40000-4440000000000000000-44000000000000002-22-20000000000000000000000000
χ738-8-880080000-88-80000000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400004-4400000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000
χ758-8-8800-400004-44000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000

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