Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×#11758090 |
| Fitting | C22×C32×H(3,𝔽3) ⋊ C22 |
| derived, Sylow | C32×H(3,𝔽3) ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11758090 |
| commutator, cosocle, hypocenter | C32×H(3,𝔽3) | C24 |
| Frattini | C3 | C22×C3⋊#1113 |
| Fitting | C22×C32×H(3,𝔽3) | C22 |
| socle | C22×C33 | D32 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C22 | |
5500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72214331 |
Past the SmallGroups library coverage — no SmallGroups id.