Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D32×#532 |
| Fitting | C32×#532 ⋊ C22 |
| Sylow | C32 ⋊ C22×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C26 |
| Frattini | C22 | C24×D32 |
| Fitting | C32×#532 | C22 |
| hypercenter | #532 | D32 |
| hypocenter | C32 | C22×#532 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
26620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#3151 |
| maximal normal subgroup of | D32×#3151 |
Past the SmallGroups library coverage — no SmallGroups id.