Finite Group Databasebeta

← Group #10827310

Character table — Group #10827310

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444466888888888888888888888888881212121616161616161624242424242424242424242448
order122222344446664444661212121222244444446688121212121212121212121212121224481212242424244444444444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111111111-1-1-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-11111-1-11-11-1-1-111-1-111-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111-11-1-1-1-1-111-1-11
χ5111111111111111111111111-1-111111111111111111111111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1111-1-111-1-11
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-11-1-1-1-111-11-111111-1-111-1
χ911111111111111-1-1-1-1111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-11-11-1-111-1-1-1-11
χ1011111111111111-1-1-1-1111111111-1-11-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-111-1-1-11-11-1-1-1-11111-1
χ1111111111111111-1-1-1-111111111-111-11111-1-1-1-1-1-1-1-11111-1-11111111-111-1-1-1-1-1-1-1-1111111-1-1-1
χ1211111111111111-1-1-1-111111111-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1111
χ1311111111111111-1-1-1-1111111-1-11-1-1111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1111-11-111-1-11111-1
χ1411111111111111-1-1-1-1111111-1-11-1-11-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11-11-11111-1-1-1-11
χ1511111111111111-1-1-1-1111111-1-1-111-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111
χ1611111111111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111111111-1-11111-1-1-1
χ172222222-2-2-2-2222000022-2-2-2-22202-2000000000000022-2-20000002-2-2000000000002-20000000
χ182222222-2-2-2-2222000022-2-2-2-2220-220000000000000-2-2220000002-2-200000000000-220000000
χ192222222-2-2-2-2222000022-2-2-2-2-2-202-2000000000000022-2-2000000-22200000000000-220000000
χ202222222-2-2-2-2222000022-2-2-2-2-2-20-220000000000000-2-222000000-222000000000002-20000000
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
χ23222222-12222-1-1-12222-1-1-1-1-1-100-2-2-2-222-2-21122-1-1-1-11111111111000-2-1-1-1-1110000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-100-2-2-2-2-2-22211-2-2-1-1-1-1111111-1-1-1-100021111-1-10000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1002-2-2222-2-2-1-1-2-211111111-1-111110002-1-111-1-10000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1002-2-22-2-222-1-12211111111-1-1-1-1-1-1000-211-1-1110000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-100-222-2222211-2-21111-1-1-1-111-1-1-1-1000-2-1-111110000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-100-222-2-2-2-2-211221111-1-1-1-1111111000211-1-1-1-10000000000000
χ292222-2-222-2-2222222-2-2-2-22-22-22200000000000022-2-20000000000-22-2000000020-20000000000
χ302222-2-222-2-2222222-2-2-2-22-22-2-2-200000000000022-2-200000000002-220000000-2020000000000
χ312222-2-222-2-22222-2-222-2-22-22-222000000000000-2-2220000000000-22-20000000-2020000000000
χ322222-2-222-2-22222-2-222-2-22-22-2-2-2000000000000-2-22200000000002-22000000020-20000000000
χ332222-2-22-222-22220000-2-2-22-2222200-20000220000000000-2-20000-2-220000000020-2000000000
χ342222-2-22-222-22220000-2-2-22-2222-20020000-2-20000000000220000-2-2200000000-202000000000
χ352222-2-22-222-22220000-2-2-22-22-2-2200-20000220000000000-2-2000022-200000000-202000000000
χ362222-2-22-222-22220000-2-2-22-22-2-2-20020000-2-2000000000022000022-20000000020-2000000000
χ372-2-222-222-22-2-2-222i−2i2i−2i-2222-2-2000000000000002i−2i2i−2i000000000000000000000000002-2002i−2i0
χ382-2-222-222-22-2-2-222i−2i2i−2i-2222-2-2000000000000002i−2i2i−2i00000000000000000000000000-2200−2i2i0
χ392-2-222-222-22-2-2-22−2i2i−2i2i-2222-2-200000000000000−2i2i−2i2i000000000000000000000000002-200−2i2i0
χ402-2-222-222-22-2-2-22−2i2i−2i2i-2222-2-200000000000000−2i2i−2i2i00000000000000000000000000-22002i−2i0
χ412-2-22-22222-2-2-2-222i−2i−2i2i2-22-2-220000002-200002i−2i2i−2i−2i2i000000000000002-22i−2i000000000000000
χ422-2-22-22222-2-2-2-222i−2i−2i2i2-22-2-22000000-220000−2i2i2i−2i−2i2i00000000000000-22−2i2i000000000000000
χ432-2-22-22222-2-2-2-22−2i2i2i−2i2-22-2-220000002-20000−2i2i−2i2i2i−2i000000000000002-2−2i2i000000000000000
χ442-2-22-22222-2-2-2-22−2i2i2i−2i2-22-2-22000000-2200002i−2i−2i2i2i−2i00000000000000-222i−2i000000000000000
χ452-2-22-22-122-2-211-12i−2i−2i2i-11-111-10000002-200−i3i32i−2i−iii−i3−33−3−i3i333−3−30000-11−ii−i3i30000000000000
χ462-2-22-22-122-2-211-12i−2i−2i2i-11-111-10000002-200i3−i32i−2i−iii−i−33−33i3−i3−3−3330000-11−iii3−i30000000000000
χ472-2-22-22-122-2-211-12i−2i−2i2i-11-111-1000000-2200−i3i3−2i2i−iii−i3−33−3−i3i3−3−33300001-1i−ii3−i30000000000000
χ482-2-22-22-122-2-211-12i−2i−2i2i-11-111-1000000-2200i3−i3−2i2i−iii−i−33−33i3−i333−3−300001-1i−i−i3i30000000000000
χ492-2-22-22-122-2-211-1−2i2i2i−2i-11-111-10000002-200−i3i3−2i2ii−i−ii−33−33−i3i3−3−3330000-11i−i−i3i30000000000000
χ502-2-22-22-122-2-211-1−2i2i2i−2i-11-111-10000002-200i3−i3−2i2ii−i−ii3−33−3i3−i333−3−30000-11i−ii3−i30000000000000
χ512-2-22-22-122-2-211-1−2i2i2i−2i-11-111-1000000-2200−i3i32i−2ii−i−ii−33−33−i3i333−3−300001-1−iii3−i30000000000000
χ522-2-22-22-122-2-211-1−2i2i2i−2i-11-111-1000000-2200i3−i32i−2ii−i−ii3−33−3i3−i3−3−33300001-1−ii−i3i30000000000000
χ53444444-2-4-4-4-4-2-2-20000-2-222220004-40000000000000-2-22200000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-22222000-44000000000000022-2-200000000000000000000000000000
χ554444-4-4-24-4-44-2-2-244-4-422-22-2200000000000000-2-222000000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2-4-44422-22-220000000000000022-2-2000000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-20000222-22-200400-40000-2-2000000000022000000000000000000000000000
χ584444-4-4-2-444-4-2-2-20000222-22-200-40040000220000000000-2-2000000000000000000000000000
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
χ634-4-444-44-44-44-4-440000-44-4-444000000000000000000000000000000000000000000000000000
χ644-4-444-4-24-44-422-24i−4i4i−4i2-2-2-22200000000000000−2i2i−2i2i000000000000000000000000000000000
χ654-4-444-4-24-44-422-2−4i4i−4i4i2-2-2-222000000000000002i−2i2i−2i000000000000000000000000000000000
χ664-4-444-4-2-44-4422-200002-222-2-20000000000−2i32i300000000002i3−2i3000000000000000000000000000
χ674-4-444-4-2-44-4422-200002-222-2-200000000002i3−2i30000000000−2i32i3000000000000000000000000000
χ684-4-44-444-4-444-4-4400004-4-444-4000000000000000000000000000000000000000000000000000
χ694-4-44-44-2-4-44422-20000-222-2-2200000000000000000023−23−232300000000000000000000000000000
χ704-4-44-44-2-4-44422-20000-222-2-22000000000000000000−232323−2300000000000000000000000000000
χ7188-8-800-40000-4440000000000000000004-400000000000000-22-2200000000000000000000000
χ7288-8-800-40000-444000000000000000000-44000000000000002-22-200000000000000000000000
χ738-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000
χ748-88-800-400004-44000000000000000000000000000000000023−23−232300000000000000000000000
χ758-88-800-400004-440000000000000000000000000000000000−232323−2300000000000000000000000

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