Finite Group Databasebeta

← Group #10833337

Character table — Group #10833337

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222244444444448888888888888888888888888812121212121212121616161616161624242424242424244848
order122222344446662244661212121222244444666666668812121212121212122244888881212242424244444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-111111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111-1111-1-1
χ4111111111111111111111111111-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11-1-1-111
χ5111111111111111111111111-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-11111-1-111111-1-1-1-1-1
χ6111111111111111111111111-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-111111
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111-1-1-1-11111-1-11111-1-1
χ911111111111111-1-1-1-111111111-111-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111-1-1-111-1-11
χ1011111111111111-1-1-1-111111111-111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-1111-1-111-1
χ1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-11-1-11111-1-1-1-1111-11-1
χ1211111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111111-1-1-11-11
χ1311111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111-1-11111-1-1-1-1-111-1
χ1411111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111-1-111-1-111111-1-11
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
χ17222222-12222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000002-1-1-1-1-1-10000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1222-2-22-2-2-1-1-1-1-1-1-1-1-2-2-1-1-1-1111100000000-21111110000000000
χ19222222-12222-1-1-12222-1-1-1-1-1-1-2-2-222-2-2-2-1-111111122-1-111111100000000-2-1-1-1-1110000000000
χ20222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-222-1-1111111-2-2-1-111-1-1-1-10000000021111-1-10000000000
χ21222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-222-22211-1-1-1-111-2-21111-1-1-1-100000000-2-1-111110000000000
χ22222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-2-2-2-2-2-211-1-1-1-111221111111100000000211-1-1-1-10000000000
χ23222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-2-2111111-1-1-2-211-1-11111000000002-1-111-1-10000000000
χ24222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22-2-2222111111-1-12211-1-1-1-1-1-100000000-211-1-1110000000000
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
χ292222-2-22-222-222222-2-2-2-2-22-22000000002200000000-2-20000000000220000000002-200-200000
χ302222-2-22-222-222222-2-2-2-2-22-22000000002200000000-2-20000000000-2-2000000000-2200200000
χ312222-2-22-222-2222-2-222-2-2-22-2200000000-2-20000000022000000000022000000000-2200-200000
χ322222-2-22-222-2222-2-222-2-2-22-2200000000-2-200000000220000000000-2-20000000002-200200000
χ332-2-222-2222-2-2-2-222-22-22-222-2-20002i−2i0002-20000002i−2i2-20000000000000002i−2i2i−2i000000000000
χ342-2-222-2222-2-2-2-222-22-22-222-2-2000−2i2i0002-2000000−2i2i2-2000000000000000−2i2i−2i2i000000000000
χ352-2-222-2222-2-2-2-22-22-222-222-2-20002i−2i000-22000000−2i2i-220000000000000002i−2i−2i2i000000000000
χ362-2-222-2222-2-2-2-22-22-222-222-2-2000−2i2i000-220000002i−2i-22000000000000000−2i2i2i−2i000000000000
χ372-2-222-22-2-222-2-2200002-2-2-2222-20000000022-2-20000000000002-22-200000000000000002-2000
χ382-2-222-22-2-222-2-2200002-2-2-2222-20000000022-2-2000000000000-22-220000000000000000-22000
χ392-2-222-22-2-222-2-2200002-2-2-222-2200000000-2-2220000000000002-22-20000000000000000-22000
χ402-2-222-22-2-222-2-2200002-2-2-222-2200000000-2-222000000000000-22-2200000000000000002-2000
χ412-2-222-2-122-2-211-12-22-2-11-1-1110002i−2i000-11−i3i3−i3i3−i3i32i−2i-11−i3i333−3−3000000000−ii−ii3−30000000000
χ422-2-222-2-122-2-211-12-22-2-11-1-1110002i−2i000-11i3−i3i3−i3i3−i32i−2i-11i3−i3−3−333000000000−ii−ii−330000000000
χ432-2-222-2-122-2-211-12-22-2-11-1-111000−2i2i000-11−i3i3−i3i3−i3i3−2i2i-11−i3i3−3−333000000000i−ii−i−330000000000
χ442-2-222-2-122-2-211-12-22-2-11-1-111000−2i2i000-11i3−i3i3−i3i3−i3−2i2i-11i3−i333−3−3000000000i−ii−i3−30000000000
χ452-2-222-2-122-2-211-1-22-22-11-1-1110002i−2i0001-1−i3i3−i3i3i3−i3−2i2i1-1i3−i333−3−3000000000−iii−i−330000000000
χ462-2-222-2-122-2-211-1-22-22-11-1-1110002i−2i0001-1i3−i3i3−i3−i3i3−2i2i1-1−i3i3−3−333000000000−iii−i3−30000000000
χ472-2-222-2-122-2-211-1-22-22-11-1-111000−2i2i0001-1−i3i3−i3i3i3−i32i−2i1-1i3−i3−3−333000000000i−i−ii3−30000000000
χ482-2-222-2-122-2-211-1-22-22-11-1-111000−2i2i0001-1i3−i3i3−i3−i3i32i−2i1-1−i3i333−3−3000000000i−i−ii−330000000000
χ492-2-22-222-22-22-2-222-2-22-22-222-2000000002-200000000-220000002-2-2200000000000002-2000000
χ502-2-22-222-22-22-2-222-2-22-22-222-2000000002-200000000-22000000-222-20000000000000-22000000
χ512-2-22-222-22-22-2-22-222-2-22-222-200000000-22000000002-20000002-2-220000000000000-22000000
χ522-2-22-222-22-22-2-22-222-2-22-222-200000000-22000000002-2000000-222-200000000000002-2000000
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
χ604-44-40040000-44-400000000000000002-2000000000000002-22-20000−2i22i2−2i22i200000000000000000
χ614-44-40040000-44-400000000000000002-2000000000000002-22-200002i2−2i22i2−2i200000000000000000
χ624-44-40040000-44-40000000000000000-2200000000000000-22-220000−2i22i22i2−2i200000000000000000
χ634-44-40040000-44-40000000000000000-2200000000000000-22-2200002i2−2i2−2i22i200000000000000000
χ644-4-444-4-2-4-44422-20000-2222-2-24-400000000-2-2220000000000000000000000000000000000000
χ654-4-444-4-2-4-44422-20000-2222-2-2-440000000022-2-20000000000000000000000000000000000000
χ664-4-44-4444-44-4-4-440000-444-4-44000000000000000000000000000000000000000000000000000
χ674-4-44-44-24-44-422-200002-2-222-200000000000000−2i32i300002i3−2i300000000000000000000000000000
χ684-4-44-44-24-44-422-200002-2-222-2000000000000002i3−2i30000−2i32i300000000000000000000000000000
χ694-4-44-44-2-44-4422-24-4-442-22-2-2200000000-22000000002-20000000000000000000000000000000
χ704-4-44-44-2-44-4422-2-444-42-22-2-22000000002-200000000-220000000000000000000000000000000
χ7188-8-800800008-8-80000000000000000000000000000000000000000000000000000000000000
χ7288-8-800-40000-4440000000000000000000000000000000023−23−23230000000000000000000000000
χ7388-8-800-40000-44400000000000000000000000000000000−232323−230000000000000000000000000
χ748-88-800-400004-4400000000000000004-400000000000000-22-220000000000000000000000000
χ758-88-800-400004-440000000000000000-44000000000000002-22-20000000000000000000000000

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