Finite Group Databasebeta

← Group #10828104

Character table — Group #10828104

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444466888888888888888888888888881212121616161616161624242424242424242424242448
order122222344446662244661212121222444444446688121212121212121212121212121224481212242424242244444444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111111111-1-1-1-1111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111-11111-1-11-1111-1-1-1-1-111-1
χ411111111111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111-1-1-11-1-1-111-1-11
χ5111111111111111111111111-1-111111111111111111111111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ7111111111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-111111-1-11
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-11-1-1-1-111-1111-1111-1-111-1
χ911111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1111-11-1-1-1-1-1-11
χ1011111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-111-1-1-1-11111111-1-1-111-1-1-11-1-1-11-1-11111-1
χ1111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-111111111111-111-1-1-1-1-1-111-1-11111-1-1-1
χ1211111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1111
χ1311111111111111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-11-1111111-1
χ1411111111111111-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-11-1111-111-1-1-1-11
χ1511111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111
χ1611111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-11111111111-1-111-1-1-1
χ172222222-2-2-2-2222000022-2-2-2-222002-20000000000000022-2-200002-2-200000000000002-200000
χ182222222-2-2-2-2222000022-2-2-2-22200-2200000000000000-2-22200002-2-20000000000000-2200000
χ192222222-2-2-2-2222000022-2-2-2-2-2-2002-20000000000000022-2-20000-2220000000000000-2200000
χ202222222-2-2-2-2222000022-2-2-2-2-2-200-2200000000000000-2-2220000-22200000000000002-200000
χ21222222-12222-1-1-12222-1-1-1-1-1-10022222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10002-1-1-1-1-1-10000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1002222-2-2-2-2-1-1-2-2-1-1-1-1-1-1-1-1-1-11111000-21111110000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-100-2-2-2-222-2-2-1-12211-1-11111111111000-2-1-1-1-1110000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-100-2-2-2-2-2-222-1-1-2-211-1-1111111-1-1-1-100021111-1-10000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-10022-2-222-2-211-2-2-1-111-1-1111111110002-1-111-1-10000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-10022-2-2-2-2221122-1-111-1-11111-1-1-1-1000-211-1-1110000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-100-2-222222211-2-2111111-1-1-1-1-1-1-1-1000-2-1-111110000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-100-2-222-2-2-2-21122111111-1-1-1-11111000211-1-1-1-10000000000000
χ292222-2-222-2-2222222-2-2-2-22-22-22200000000220000-2-20000000000-22-200000002000-200000000
χ302222-2-222-2-2222222-2-2-2-22-22-2-2-200000000220000-2-200000000002-220000000-2000200000000
χ312222-2-222-2-22222-2-222-2-22-22-22200000000-2-20000220000000000-22-20000000-2000200000000
χ322222-2-222-2-22222-2-222-2-22-22-2-2-200000000-2-200002200000000002-2200000002000-200000000
χ332222-2-22-222-22220000-2-2-22-22222-200000000002200-2-200000000-2-22000000002000-20000000
χ342222-2-22-222-22220000-2-2-22-2222-220000000000-2-2002200000000-2-2200000000-200020000000
χ352222-2-22-222-22220000-2-2-22-22-2-22-200000000002200-2-20000000022-200000000-200020000000
χ362222-2-22-222-22220000-2-2-22-22-2-2-220000000000-2-200220000000022-2000000002000-20000000
χ372-2-222-2222-2-2-22-22-22-2-222-2-220000002i−2i002-22i−2i002-2000000000000002i−2i2i−2i000000000000000
χ382-2-222-2222-2-2-22-22-22-2-222-2-22000000−2i2i002-2−2i2i002-200000000000000−2i2i−2i2i000000000000000
χ392-2-222-2222-2-2-22-2-22-22-222-2-220000002i−2i00-22−2i2i00-22000000000000002i−2i−2i2i000000000000000
χ402-2-222-2222-2-2-22-2-22-22-222-2-22000000−2i2i00-222i−2i00-2200000000000000−2i2i2i−2i000000000000000
χ412-2-222-2-122-2-21-112-22-21-1-111-10000002i−2i00-112i−2i3−3-113−33−33−3−i3−i3i3i30000−ii−ii−i3i30000000000000
χ422-2-222-2-122-2-21-112-22-21-1-111-10000002i−2i00-112i−2i−33-11−33−33−33i3i3−i3−i30000−ii−iii3−i30000000000000
χ432-2-222-2-122-2-21-112-22-21-1-111-1000000−2i2i00-11−2i2i3−3-113−33−33−3i3i3−i3−i30000i−ii−ii3−i30000000000000
χ442-2-222-2-122-2-21-112-22-21-1-111-1000000−2i2i00-11−2i2i−33-11−33−33−33−i3−i3i3i30000i−ii−i−i3i30000000000000
χ452-2-222-2-122-2-21-11-22-221-1-111-10000002i−2i001-1−2i2i3−31-13−3−33−33i3i3−i3−i30000−iii−i−i3i30000000000000
χ462-2-222-2-122-2-21-11-22-221-1-111-10000002i−2i001-1−2i2i−331-1−333−33−3−i3−i3i3i30000−iii−ii3−i30000000000000
χ472-2-222-2-122-2-21-11-22-221-1-111-1000000−2i2i001-12i−2i3−31-13−3−33−33−i3−i3i3i30000i−i−iii3−i30000000000000
χ482-2-222-2-122-2-21-11-22-221-1-111-1000000−2i2i001-12i−2i−331-1−333−33−3i3i3−i3−i30000i−i−ii−i3i30000000000000
χ492-2-22-2222-22-2-22-22-2-222-222-2-200000000002-20000-2200000000000000000000002i−2i0000002i−2i0
χ502-2-22-2222-22-2-22-22-2-222-222-2-200000000002-20000-220000000000000000000000−2i2i000000−2i2i0
χ512-2-22-2222-22-2-22-2-222-22-222-2-20000000000-2200002-200000000000000000000002i−2i000000−2i2i0
χ522-2-22-2222-22-2-22-2-222-22-222-2-20000000000-2200002-20000000000000000000000−2i2i0000002i−2i0
χ53444444-2-4-4-4-4-2-2-20000-2-2222200004-400000000000000-2-222000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-222220000-440000000000000022-2-2000000000000000000000000000
χ554444-4-4-24-4-44-2-2-244-4-422-22-220000000000-2-2000022000000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2-4-44422-22-220000000000220000-2-2000000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-20000222-22-2004-40000000000-2-200220000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-20000222-22-200-4400000000002200-2-20000000000000000000000000000000
χ5944-4-400400004-4-400000000004-40000002-2000000000000002-22-20000000000000000002-2000
χ6044-4-400400004-4-400000000004-4000000-2200000000000000-22-22000000000000000000-22000
χ6144-4-400400004-4-40000000000-440000002-2000000000000002-22-2000000000000000000-22000
χ6244-4-400400004-4-40000000000-44000000-2200000000000000-22-220000000000000000002-2000
χ634-4-444-44-4-444-44-40000-44-444-4000000000000000000000000000000000000000000000000000
χ644-4-444-4-2-4-4442-2200002-22-2-220000000000000000000023−23−2323000000000000000000000000000
χ654-4-444-4-2-4-4442-2200002-22-2-2200000000000000000000−232323−23000000000000000000000000000
χ664-4-44-444-44-44-44-400004-4-4-444000000000000000000000000000000000000000000000000000
χ674-4-44-44-24-44-42-224-4-44-22-2-2220000000000-2200002-2000000000000000000000000000000000
χ684-4-44-44-24-44-42-22-444-4-22-2-22200000000002-20000-22000000000000000000000000000000000
χ694-4-44-44-2-44-442-220000-2222-2-20000000000000023−2300−23230000000000000000000000000000000
χ704-4-44-44-2-44-442-220000-2222-2-200000000000000−23230023−230000000000000000000000000000000
χ7188-8-800-40000-4440000000000000000004-400000000000000-22-2200000000000000000000000
χ7288-8-800-40000-444000000000000000000-44000000000000002-22-200000000000000000000000
χ738-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000
χ748-88-800-4000044-40000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000
χ758-88-800-4000044-400000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000

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