Finite Group Databasebeta

← Group #82253

Character table — Group #82253

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222222234444444466666661212121212121212224444444466661212121212121212121212121212121212121212444444442444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11-1-11
χ61111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ71111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-1
χ81111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-11
χ9111111111-1-1-1-1111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ10111111111-1-1-1-1111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ11111111111-1-1-1-11111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ12111111111-1-1-1-11111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ13111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-11-11
χ14111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11-11-1
χ15111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111-11-1
χ16111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-11-11
χ1722222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1822222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-1-1-1-1-1111111111111000000000000
χ1922222222-12222-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2-2-222-1-1-1-1-1-1-1-11111-1-1-1-111111111000000000000
χ2022222222-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-2-21111-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ2122222222-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-1111111111111-1-1-1-11111000000000000
χ2222222222-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222111111111111-1-1-1-11111-1-1-1-1000000000000
χ2322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-222-2-2-1-1-1-11111-1-1-1-111111111-1-1-1-1000000000000
χ2422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-222222211111111-1-1-1-1-1-1-1-1-1-1-1-11111000000000000
χ2522-22-2-2-22200002i2i−2i−2i22-2-22-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000002-22i−2i00000000
χ2622-22-2-2-22200002i2i−2i−2i22-2-22-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000-22−2i2i00000000
χ2722-22-2-2-2220000−2i−2i2i2i22-2-22-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000002-2−2i2i00000000
χ2822-22-2-2-2220000−2i−2i2i2i22-2-22-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000-222i−2i00000000
χ2922-2-2-222-222i2i−2i−2i00002-22-2-22-2000000002-20000002i−2i22-2-22i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ3022-2-2-222-222i2i−2i−2i00002-22-2-22-200000000-22000000−2i2i-2-2222i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ3122-2-2-222-22−2i−2i2i2i00002-22-2-22-2000000002-2000000−2i2i22-2-2−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ3222-2-2-222-22−2i−2i2i2i00002-22-2-22-200000000-220000002i−2i-2-222−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ3322-2-2-222-2-12i2i−2i−2i0000-11-111-11−i3−i3i3i3−i3−i3i3i32-20000002i−2i-1-111−i−iii33−3−3−i−iii−i3−i3i3i333−3−3000000000000
χ3422-2-2-222-2-12i2i−2i−2i0000-11-111-11−i3−i3i3i3−i3−i3i3i3-22000000−2i2i11-1-1−i−iii33−3−3ii−i−ii3i3−i3−i3−3−333000000000000
χ3522-2-2-222-2-12i2i−2i−2i0000-11-111-11i3i3−i3−i3i3i3−i3−i32-20000002i−2i-1-111−i−iii−3−333−i−iiii3i3−i3−i3−3−333000000000000
χ3622-2-2-222-2-12i2i−2i−2i0000-11-111-11i3i3−i3−i3i3i3−i3−i3-22000000−2i2i11-1-1−i−iii−3−333ii−i−i−i3−i3i3i333−3−3000000000000
χ3722-2-2-222-2-1−2i−2i2i2i0000-11-111-11−i3−i3i3i3−i3−i3i3i32-2000000−2i2i-1-111ii−i−i−3−333ii−i−i−i3−i3i3i3−3−333000000000000
χ3822-2-2-222-2-1−2i−2i2i2i0000-11-111-11−i3−i3i3i3−i3−i3i3i3-220000002i−2i11-1-1ii−i−i−3−333−i−iiii3i3−i3−i333−3−3000000000000
χ3922-2-2-222-2-1−2i−2i2i2i0000-11-111-11i3i3−i3−i3i3i3−i3−i32-2000000−2i2i-1-111ii−i−i33−3−3ii−i−ii3i3−i3−i333−3−3000000000000
χ4022-2-2-222-2-1−2i−2i2i2i0000-11-111-11i3i3−i3−i3i3i3−i3−i3-220000002i−2i11-1-1ii−i−i33−3−3−i−iii−i3−i3i3i3−3−333000000000000
χ412-222-2-22-2200002i−2i2i−2i-222-2-2-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000002-22i−2i0000
χ422-222-2-22-2200002i−2i2i−2i-222-2-2-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000-22−2i2i0000
χ432-222-2-22-220000−2i2i−2i2i-222-2-2-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000002-2−2i2i0000
χ442-222-2-22-220000−2i2i−2i2i-222-2-2-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000-222i−2i0000
χ452-22-2-22-2222-22-20000-2-2-2-222200000000002-22-2000000002-22-2000000002-22-22-22-2000000000000
χ462-22-2-22-2222-22-20000-2-2-2-22220000000000-22-22000000002-22-200000000-22-22-22-22000000000000
χ472-22-2-22-222-22-220000-2-2-2-222200000000002-2-2200000000-22-2200000000-22-222-22-2000000000000
χ482-22-2-22-222-22-220000-2-2-2-22220000000000-222-200000000-22-22000000002-22-2-22-22000000000000
χ492-22-2-22-22-12-22-200001111-1-1-1−i3i3i3−i3i3−i3−i3i3002-22-20000−i3i3−i3i3-11-11−i3i3−i3i3−i3i3−i3i3-11-11-11-11000000000000
χ502-22-2-22-22-12-22-200001111-1-1-1−i3i3i3−i3i3−i3−i3i300-22-220000i3−i3i3−i3-11-11−i3i3−i3i3i3−i3i3−i31-11-11-11-1000000000000
χ512-22-2-22-22-12-22-200001111-1-1-1i3−i3−i3i3−i3i3i3−i3002-22-20000i3−i3i3−i3-11-11i3−i3i3−i3i3−i3i3−i3-11-11-11-11000000000000
χ522-22-2-22-22-12-22-200001111-1-1-1i3−i3−i3i3−i3i3i3−i300-22-220000−i3i3−i3i3-11-11i3−i3i3−i3−i3i3−i3i31-11-11-11-1000000000000
χ532-22-2-22-22-1-22-2200001111-1-1-1−i3i3i3−i3i3−i3−i3i3002-2-220000i3−i3i3−i31-11-1i3−i3i3−i3−i3i3−i3i31-11-1-11-11000000000000
χ542-22-2-22-22-1-22-2200001111-1-1-1−i3i3i3−i3i3−i3−i3i300-222-20000−i3i3−i3i31-11-1i3−i3i3−i3i3−i3i3−i3-11-111-11-1000000000000
χ552-22-2-22-22-1-22-2200001111-1-1-1i3−i3−i3i3−i3i3i3−i3002-2-220000−i3i3−i3i31-11-1−i3i3−i3i3i3−i3i3−i31-11-1-11-11000000000000
χ562-22-2-22-22-1-22-2200001111-1-1-1i3−i3−i3i3−i3i3i3−i300-222-20000i3−i3i3−i31-11-1−i3i3−i3i3−i3i3−i3i3-11-111-11-1000000000000
χ572-2-2222-2-222i−2i−2i2i2-2-22-22-22-22-22-22-2-22-220000002i−2i0000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ582-2-2222-2-222i−2i−2i2i-222-2-22-22-22-2-22-222-22-2000000−2i2i0000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ592-2-2222-2-22−2i2i2i−2i2-2-22-22-22-22-22-22-2-22-22000000−2i2i000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ602-2-2222-2-22−2i2i2i−2i-222-2-22-22-22-2-22-222-22-20000002i−2i000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ612-2-2222-2-2-12i−2i−2i2i2-2-221-11-11-11-11-111-11-10000002i−2i00−i3i3i3−i3−iii−i−iii−i3−3−33−i3i3i3−i33−3−33000000000000
χ622-2-2222-2-2-12i−2i−2i2i2-2-221-11-11-11-11-111-11-10000002i−2i00i3−i3−i3i3−iii−i−iii−i−333−3i3−i3−i3i3−333−3000000000000
χ632-2-2222-2-2-12i−2i−2i2i-222-21-11-11-111-11-1-11-11000000−2i2i00−i3i3i3−i3−iii−ii−i−ii3−3−33i3−i3−i3i3−333−3000000000000
χ642-2-2222-2-2-12i−2i−2i2i-222-21-11-11-111-11-1-11-11000000−2i2i00i3−i3−i3i3−iii−ii−i−ii−333−3−i3i3i3−i33−3−33000000000000
χ652-2-2222-2-2-1−2i2i2i−2i2-2-221-11-11-11-11-111-11-1000000−2i2i00−i3i3i3−i3i−i−iii−i−ii−333−3−i3i3i3−i3−333−3000000000000
χ662-2-2222-2-2-1−2i2i2i−2i2-2-221-11-11-11-11-111-11-1000000−2i2i00i3−i3−i3i3i−i−iii−i−ii3−3−33i3−i3−i3i33−3−33000000000000
χ672-2-2222-2-2-1−2i2i2i−2i-222-21-11-11-111-11-1-11-110000002i−2i00−i3i3i3−i3i−i−ii−iii−i−333−3i3−i3−i3i33−3−33000000000000
χ682-2-2222-2-2-1−2i2i2i−2i-222-21-11-11-111-11-1-11-110000002i−2i00i3−i3−i3i3i−i−ii−iii−i3−3−33−i3i3i3−i3−333−3000000000000
χ69444-44-4-4-44000000004-4-44-4-44000000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4-200000000-222-222-22323−23−23−23−2323230000000000000000000000000000000000000000000000
χ71444-44-4-4-4-200000000-222-222-2−23−2323232323−23−230000000000000000000000000000000000000000000000
χ7244-44-4-4-44-200004i4i−4i−4i-2-222-222−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000
χ7344-44-4-4-44-20000−4i−4i4i4i-2-222-2222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000
χ744-444-4-44-4-200004i−4i4i−4i2-2-2222-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ754-444-4-44-4-20000−4i4i−4i4i2-2-2222-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ764-4-4-44-444400000000-4-4444-4-4000000000000000000000000000000000000000000000000000000
χ774-4-4-44-444-20000000022-2-2-22223−23−232323−23−23230000000000000000000000000000000000000000000000
χ784-4-4-44-444-20000000022-2-2-222−232323−23−232323−230000000000000000000000000000000000000000000000

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