Finite Group Databasebeta

← Group #67721

Character table — Group #67721

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222222244444444444444888888888888121212121212121224242424
order1222223444466666668888881212121224242424242424244444121212121212121216161616161616164444
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-111-1-1111-1-11-1-1-1-1-1-1111-1-111111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ61111-1-111-1-1111-1-11-1-1-1-1-1-1111-1-111111-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111
χ71111-1-111-1-1111-1-11-1-1-1-1-1-1111-1-111111-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ81111-1-111-1-1111-1-11-1-1-1-1-1-1111-1-111111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ911-1-11-11-11-11-1-1111-1-1-1-1111-1-11-1111-1-111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011-1-11-11-11-11-1-1111-1-1-1-1111-1-11-1111-1-111-1-1i−ii−iii−i−iii−i−i-1-111-1-111−ii−ii
χ1111-1-11-11-11-11-1-1111-1-1-1-1111-1-11-1111-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii
χ1211-1-11-11-11-11-1-1111-1-1-1-1111-1-11-1111-1-111-1-1−ii−ii−i−iii−i−iii-1-111-1-111i−ii−i
χ1311-1-1-111-1-111-1-1-1-111111-1-11-1-1-11111-1-1-1-1111-1-1111-1-1-1-111ii−i−i−i−iii−iii−i
χ1411-1-1-111-1-111-1-1-1-111111-1-11-1-1-11111-1-1-1-1111-1-1111-1-1-1-111−i−iiiii−i−ii−i−ii
χ1511-1-1-111-1-111-1-1-1-111111-1-11-1-1-11111-1-1-1-111-111-1-1-11111-1-1ii−i−i−i−iiii−i−ii
χ1611-1-1-111-1-111-1-1-1-111111-1-11-1-1-11111-1-1-1-111-111-1-1-11111-1-1−i−iiiii−i−i−iii−i
χ17222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222-2-2-2-22222222000000-2-2-2-2000000000000000000002−22−22−22−20000
χ192222222-2-2-2-22222222000000-2-2-2-200000000000000000000−22−22−22−220000
χ20222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ21222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ242222-2-222-2-2222-2-22-2-22222-2-22-2-22-2-2-2-22222000000000000000000000000
χ252222-2-22-222-222-2-22-2-2000000-222-200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ262222-2-22-222-222-2-22-2-2000000-222-200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ272222-2-2-12-2-22-1-111-1112222-2-2-111-11111-1-1-1-100003−33−3−33−33000000000000
χ282222-2-2-12-2-22-1-111-1112222-2-2-111-11111-1-1-1-10000−33−333−33−3000000000000
χ292222-2-2-12-2-22-1-111-111-2-2-2-222-111-1-1-1-1-111112i2i−2i−2i−i−i−i−iiiii000000000000
χ302222-2-2-12-2-22-1-111-111-2-2-2-222-111-1-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i000000000000
χ3122-2-22-222-22-2-2-2222-2-20000002-22-2000000000000000000002−2−222−2−220000
χ3222-2-22-222-22-2-2-2222-2-20000002-22-200000000000000000000−222−2−222−20000
χ3322-2-22-22-22-22-2-2222-2-222-2-2-22-22-22-2-222-2-222000000000000000000000000
χ3422-2-22-2-1-22-2211-1-1-11122-2-2-221-11-111-1-111-1-100003−3−333−3−33000000000000
χ3522-2-22-2-1-22-2211-1-1-11122-2-2-221-11-111-1-111-1-10000−333−3−333−3000000000000
χ3622-2-22-2-1-22-2211-1-1-111-2-2222-21-11-1-1-111-1-1112i−2i2i−2i−i−iii−i−iii000000000000
χ3722-2-22-2-1-22-2211-1-1-111-2-2222-21-11-1-1-111-1-111−2i2i−2i2iii−i−iii−i−i000000000000
χ3822-2-2-22222-2-2-2-2-2-222200000022-2-200000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ3922-2-2-22222-2-2-2-2-2-222200000022-2-200000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ4022-2-2-222-2-222-2-2-2-2222-2-222-22-2-222-2-22222-2-2000000000000000000000000
χ4122-2-2-22-1-2-2221111-1-1-122-2-22-211-1-1-1-11111-1-12-2-22-1-11111-1-1000000000000
χ4222-2-2-22-1-2-2221111-1-1-122-2-22-211-1-1-1-11111-1-1-222-211-1-1-1-111000000000000
χ4322-2-2-22-1-2-2221111-1-1-1-2-222-2211-1-111-1-1-1-1110000−i3i3i3−i3i3−i3−i3i3000000000000
χ4422-2-2-22-1-2-2221111-1-1-1-2-222-2211-1-111-1-1-1-1110000i3−i3−i3i3−i3i3i3−i3000000000000
χ45444444-2-4-4-4-4-2-2-2-2-2-2-2000000222200000000000000000000000000000000
χ464444-4-4-2-444-4-2-222-2220000002-2-2200000000000000000000000000000000
χ4744-4-44-4-24-44-422-2-2-222000000-22-2200000000000000000000000000000000
χ4844-4-4-44-244-4-42222-2-2-2000000-2-22200000000000000000000000000000000
χ494-44-400400004-400-400−2i22i2−2i22i20000000000−2i22i2−2i22i2000000000000000000000000
χ504-44-400400004-400-4002i2−2i22i2−2i200000000002i2−2i22i2−2i2000000000000000000000000
χ514-44-400-20000-22−2i32i32−2i32i3−2i22i2−2i22i20000006−66−6i2−i2i2−i2000000000000000000000000
χ524-44-400-20000-22−2i32i32−2i32i32i2−2i22i2−2i2000000−66−66−i2i2−i2i2000000000000000000000000
χ534-44-400-20000-222i3−2i322i3−2i3−2i22i2−2i22i2000000−66−66i2−i2i2−i2000000000000000000000000
χ544-44-400-20000-222i3−2i322i3−2i32i2−2i22i2−2i20000006−66−6−i2i2−i2i2000000000000000000000000
χ554-4-440040000-4400-400−2i22i22i2−2i200000000002i2−2i2−2i22i2000000000000000000000000
χ564-4-440040000-4400-4002i2−2i2−2i22i20000000000−2i22i22i2−2i2000000000000000000000000
χ574-4-4400-200002-2−2i32i322i3−2i3−2i22i22i2−2i2000000−666−6−i2i2i2−i2000000000000000000000000
χ584-4-4400-200002-2−2i32i322i3−2i32i2−2i2−2i22i20000006−6−66i2−i2−i2i2000000000000000000000000
χ594-4-4400-200002-22i3−2i32−2i32i3−2i22i22i2−2i20000006−6−66−i2i2i2−i2000000000000000000000000
χ604-4-4400-200002-22i3−2i32−2i32i32i2−2i2−2i22i2000000−666−6i2−i2−i2i2000000000000000000000000

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