Finite Group Databasebeta

← Group #10827763

Character table — Group #10827763

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112222222224444444444488888888888888888888121212121212161616161616161616162424242424242424244848
order12222222236444466666662244444466121212121212121212122244444461212121212121224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-11-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-11111-1-1-1-1
χ411111111111111111111111-11-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-1-11111
χ51111111111111111111111-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1
χ61111111111111111111111-11-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-111-1-1
χ911111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111-1-111-1-111-1-1-1-1-1111-1
χ1011111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-111111-1-1-11
χ1111111111111-1-1-1-111111111-11-1-1-111-1-1-1-1-1-1-1-11111111111-1111-1-1-1-111111-1-1-1-1-1-1-11
χ1211111111111-1-1-1-111111111-11-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111111-1
χ1311111111111-1-1-1-11111111-11-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-111-1-1-111-1-111-11
χ1411111111111-1-1-1-11111111-11-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-111111-1-111-1-11-1
χ1511111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1-1111-1-1-1-11-1
χ1611111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-11111-1-111-1-1-11111-11
χ17222222222-1-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-100000000000
χ18222222222-1-12222-1-1-1-1-1-1-12-22-222-2-21111-1-1-1-11111000000-2-2-1-1-1-1111100000000000
χ19222222222-1-12222-1-1-1-1-1-1-1-22-22-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-21111111100000000000
χ20222222222-1-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-11111000000221111-1-1-1-100000000000
χ21222222222-1-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1111111110000002-2-1-111-1-11100000000000
χ22222222222-1-1-2-2-2-2-1-1-1-1-1-1-12-22-2-2-22211111111-1-1-1-1000000-22-1-11111-1-100000000000
χ23222222222-1-1-2-2-2-2-1-1-1-1-1-1-1-22-2222-2-2-1-1-1-111111111000000-2211-1-111-1-100000000000
χ24222222222-1-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-10000002-211-1-1-1-11100000000000
χ252222-22-2-2-2222i2i−2i−2i22-22-2-2-20000000000002i2i−2i−2i000000000000000000002-202i−2i000000
χ262222-22-2-2-2222i2i−2i−2i22-22-2-2-20000000000002i2i−2i−2i00000000000000000000-220−2i2i000000
χ272222-22-2-2-222−2i−2i2i2i22-22-2-2-2000000000000−2i−2i2i2i000000000000000000002-20−2i2i000000
χ282222-22-2-2-222−2i−2i2i2i22-22-2-2-2000000000000−2i−2i2i2i00000000000000000000-2202i−2i000000
χ29222-22-22-2-2222i−2i2i−2i2-22-22-2-220-202i−2i0000002i−2i2i−2i0000000000002-22i−2i000000000000000
χ30222-22-22-2-2222i−2i2i−2i2-22-22-2-2-2020−2i2i0000002i−2i2i−2i000000000000-22−2i2i000000000000000
χ31222-22-22-2-222−2i2i−2i2i2-22-22-2-220-20−2i2i000000−2i2i−2i2i0000000000002-2−2i2i000000000000000
χ32222-22-22-2-222−2i2i−2i2i2-22-22-2-2-20202i−2i000000−2i2i−2i2i000000000000-222i−2i000000000000000
χ33222-22-22-2-2-1-12i−2i2i−2i-11-11-11120-202i−2i00−i3i3−i3i3−ii−ii33−3−300000000-11−ii−i3i33−300000000000
χ34222-22-22-2-2-1-12i−2i2i−2i-11-11-11120-202i−2i00i3−i3i3−i3−ii−ii−3−33300000000-11−iii3−i3−3300000000000
χ35222-22-22-2-2-1-12i−2i2i−2i-11-11-111-2020−2i2i00−i3i3−i3i3−ii−ii33−3−3000000001-1i−ii3−i3−3300000000000
χ36222-22-22-2-2-1-12i−2i2i−2i-11-11-111-2020−2i2i00i3−i3i3−i3−ii−ii−3−333000000001-1i−i−i3i33−300000000000
χ37222-22-22-2-2-1-1−2i2i−2i2i-11-11-11120-20−2i2i00−i3i3−i3i3i−ii−i−3−33300000000-11i−i−i3i3−3300000000000
χ38222-22-22-2-2-1-1−2i2i−2i2i-11-11-11120-20−2i2i00i3−i3i3−i3i−ii−i33−3−300000000-11i−ii3−i33−300000000000
χ39222-22-22-2-2-1-1−2i2i−2i2i-11-11-111-20202i−2i00−i3i3−i3i3i−ii−i−3−333000000001-1−iii3−i33−300000000000
χ40222-22-22-2-2-1-1−2i2i−2i2i-11-11-111-20202i−2i00i3−i3i3−i3i−ii−i33−3−3000000001-1−ii−i3i3−3300000000000
χ41222-2-2-2-222222-2-222-2-2-2-2220000000000002-2-22000022-2-2000000000000000002-20000
χ42222-2-2-2-222222-2-222-2-2-2-2220000000000002-2-220000-2-22200000000000000000-220000
χ43222-2-2-2-22222-222-22-2-2-2-222000000000000-222-2000022-2-200000000000000000-220000
χ44222-2-2-2-22222-222-22-2-2-2-222000000000000-222-20000-2-222000000000000000002-20000
χ4522-22-2-22-22220000-2-222-2-220000002-2000000002-22-22-22-222000000000000-200000000
χ4622-22-2-22-22220000-2-222-2-220000002-2000000002-22-2-22-22-2-2000000000000200000000
χ4722-22-2-22-22220000-2-222-2-22000000-2200000000-22-222-22-2-2-2000000000000200000000
χ4822-22-2-22-22220000-2-222-2-22000000-2200000000-22-22-22-2222000000000000-200000000
χ4922-2-222-2-22220000-22-2-22-22020-2000022-2-2000000002-2-2200000000000000000002-200
χ5022-2-222-2-22220000-22-2-22-22020-2000022-2-200000000-222-20000000000000000000-2200
χ5122-2-222-2-22220000-22-2-22-220-2020000-2-222000000002-2-220000000000000000000-2200
χ5222-2-222-2-22220000-22-2-22-220-2020000-2-22200000000-222-200000000000000000002-200
χ534444-44-4-4-4-2-24i4i−4i−4i-2-22-2222000000000000−2i−2i2i2i0000000000000000000000000000000
χ544444-44-4-4-4-2-2−4i−4i4i4i-2-22-22220000000000002i2i−2i−2i0000000000000000000000000000000
χ55444-4-4-4-444-2-24-4-44-22222-2-2000000000000-222-20000000000000000000000000000000
χ56444-4-4-4-444-2-2-444-4-22222-2-20000000000002-2-220000000000000000000000000000000
χ5744-444-4-44-4440000-4-4-4444-400000000000000000000000000000000000000000000000
χ5844-444-4-44-4-2-20000222-2-2-2200000000−2i32i32i3−2i300000000000000000000000000000000000
χ5944-444-4-44-4-2-20000222-2-2-22000000002i3−2i3−2i32i300000000000000000000000000000000000
χ6044-44-4-44-44-2-2000022-2-222-20000004-400000000-22-22000000000000000000000000000
χ6144-44-4-44-44-2-2000022-2-222-2000000-44000000002-22-2000000000000000000000000000
χ6244-4-444-4-44-2-200002-222-22-2040-40000-2-22200000000000000000000000000000000000
χ6344-4-444-4-44-2-200002-222-22-20-404000022-2-200000000000000000000000000000000000
χ6444-4-4-4444-4440000-444-4-44-400000000000000000000000000000000000000000000000
χ6544-4-4-4444-4-2-200002-2-222-22000000000000000023−23−2323000000000000000000000000000
χ6644-4-4-4444-4-2-200002-2-222-220000000000000000−232323−23000000000000000000000000000
χ678-800000008-8000000000000000000000000000000000004i−4i000000000000000000000
χ688-800000008-800000000000000000000000000000000000−4i4i000000000000000000000
χ6916-160000000-880000000000000000000000000000000000000000000000000000000000

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