Finite Group Databasebeta

← Group #67727

Character table — Group #67727

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222222244444444444444888888888888121212121212121224242424
order124422234446668888121212126688121224242424242424244444121212121212121216161616161616168888
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
χ511111-1-11-1-111-1-1-1-1-1-111-1-11-111-111111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ611111-1-11-1-111-1-1-1-1-1-111-1-11-111-111111-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111
χ711111-1-11-1-111-1-1-1-1-1-111-1-11-111-111111-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ811111-1-11-1-111-1-1-1-1-1-111-1-11-111-111111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ911-1-1-11-111-111-1-1-1-111-1-111-111-1-1111-1-111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011-1-1-11-111-111-1-1-1-111-1-111-111-1-1111-1-111-1-1i−ii−iii−i−iii−i−i-1-111-1-111−ii−ii
χ1111-1-1-11-111-111-1-1-1-111-1-111-111-1-1111-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii
χ1211-1-1-11-111-111-1-1-1-111-1-111-111-1-1111-1-111-1-1−ii−ii−i−iii−i−iii-1-111-1-111i−ii−i
χ1311-1-1-1-111-11111111-1-1-1-1-1-1-1-11-11111-1-1-1-1111-1-1111-1-1-1-111ii−i−i−i−iii−iii−i
χ1411-1-1-1-111-11111111-1-1-1-1-1-1-1-11-11111-1-1-1-1111-1-1111-1-1-1-111−i−iiiii−i−ii−i−ii
χ1511-1-1-1-111-11111111-1-1-1-1-1-1-1-11-11111-1-1-1-111-111-1-1-11111-1-1ii−i−i−i−iiii−i−ii
χ1611-1-1-1-111-11111111-1-1-1-1-1-1-1-11-11111-1-1-1-111-111-1-1-11111-1-1−i−iiiii−i−i−iii−i
χ1722222222222222-2-2-2-2222222-2-222-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222-1222-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ192222222-1222-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ202222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2-1-1111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2-1-1111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ2222222-2-22-2-222-2-2222222-2-22-2-2-2-22-2-2-2-22222000000000000000000000000
χ2322222-2-2-1-2-22-1112222-1-111-11-2-21-11111-1-1-1-100003−33−3−33−33000000000000
χ2422222-2-2-1-2-22-1112222-1-111-11-2-21-11111-1-1-1-10000−33−333−33−3000000000000
χ2522222-2-2-1-2-22-111-2-2-2-2-1-111-11221-1-1-1-1-111112i2i−2i−2i−i−i−i−iiiii000000000000
χ2622222-2-2-1-2-22-111-2-2-2-2-1-111-11221-1-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i000000000000
χ272222-22-22-22-22-2-2000022-2-2-22002-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ282222-22-22-22-22-2-2000022-2-2-22002-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ292222-2-2222-2-222200002222-2-200-2-2000000000000000000002−22−2−22−220000
χ302222-2-2222-2-222200002222-2-200-2-200000000000000000000−22−222−22−20000
χ3122-2-22222-2-2-22220000-2-2-2-22200-2-200000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ3222-2-22222-2-2-22220000-2-2-2-22200-2-200000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ3322-2-22-2-2222-22-2-20000-2-2222-2002-2000000000000000000002−2−22−222−20000
χ3422-2-22-2-2222-22-2-20000-2-2222-2002-200000000000000000000−222−22−2−220000
χ3522-2-2-22-222-222-2-222-2-2-2-222-22-22-22-2-222-2-222000000000000000000000000
χ3622-2-2-22-2-12-22-11122-2-211-1-11-1-221-111-1-111-1-100003−3−333−3−33000000000000
χ3722-2-2-22-2-12-22-11122-2-211-1-11-1-221-111-1-111-1-10000−333−3−333−3000000000000
χ3822-2-2-22-2-12-22-111-2-22211-1-11-12-21-1-1-111-1-1112i−2i2i−2i−i−iii−i−iii000000000000
χ3922-2-2-22-2-12-22-111-2-22211-1-11-12-21-1-1-111-1-111−2i2i−2i2iii−i−iii−i−i000000000000
χ4022-2-2-2-222-222222-2-222-2-2-2-2-2-2-2222-2-22222-2-2000000000000000000000000
χ4122-2-2-2-22-1-222-1-1-122-2-21111112-2-1-1-1-11111-1-12-2-22-1-11111-1-1000000000000
χ4222-2-2-2-22-1-222-1-1-122-2-21111112-2-1-1-1-11111-1-1-222-211-1-1-1-111000000000000
χ4322-2-2-2-22-1-222-1-1-1-2-222111111-22-1-111-1-1-1-1110000−i3i3i3−i3i3−i3−i3i3000000000000
χ4422-2-2-2-22-1-222-1-1-1-2-222111111-22-1-111-1-1-1-1110000i3−i3−i3i3−i3i3i3−i3000000000000
χ454444-44-4-2-44-4-2220000-2-2222-200-2200000000000000000000000000000000
χ464444-4-44-24-4-4-2-2-20000-2-2-2-222002200000000000000000000000000000000
χ4744-4-4444-2-4-4-4-2-2-200002222-2-2002200000000000000000000000000000000
χ4844-4-44-4-4-244-4-222000022-2-2-2200-2200000000000000000000000000000000
χ494-44i−4i0004000-400−2i22i222−224i−4i00000000000022−22−2i22i2000000000000000000000000
χ504-44i−4i0004000-4002i2−2i2−22224i−4i000000000000−22222i2−2i2000000000000000000000000
χ514-44i−4i000-20002−2i32i3−2i22i222−22−2i2i23−230000006−6i6−i6−22i2−i2000000000000000000000000
χ524-44i−4i000-20002−2i32i32i2−2i2−2222−2i2i23−23000000−66−i6i62−2−i2i2000000000000000000000000
χ534-44i−4i000-200022i3−2i3−2i22i222−22−2i2i−2323000000−66−i6i6−22i2−i2000000000000000000000000
χ544-44i−4i000-200022i3−2i32i2−2i2−2222−2i2i−23230000006−6i6−i62−2−i2i2000000000000000000000000
χ554-4−4i4i0004000-400−2i22i2−2222−4i4i000000000000−2222−2i22i2000000000000000000000000
χ564-4−4i4i0004000-4002i2−2i222−22−4i4i00000000000022−222i2−2i2000000000000000000000000
χ574-4−4i4i000-20002−2i32i3−2i22i2−22222i−2i−23230000006−6−i6i62−2i2−i2000000000000000000000000
χ584-4−4i4i000-20002−2i32i32i2−2i222−222i−2i−2323000000−66i6−i6−22−i2i2000000000000000000000000
χ594-4−4i4i000-200022i3−2i3−2i22i2−22222i−2i23−23000000−66i6−i62−2i2−i2000000000000000000000000
χ604-4−4i4i000-200022i3−2i32i2−2i222−222i−2i23−230000006−6−i6i6−22−i2i2000000000000000000000000

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