Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C2×D9×#392 |
| Fitting | C2×C9×#392 ⋊ C2 |
| Sylow | C9 ⋊ C22×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D9 |
| commutator, cosocle | C23×C9 | C25 |
| Frattini | C23×C3 | C24×D3 |
| Fitting | C2×C9×#392 | C2 |
| socle | C24×C3 | C23×D3 |
| hypercenter | C2×#392 | D9 |
| hypocenter | C9 | C22×#392 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C24 ◁ C2×#392 | |
20469 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×#15258 |
| maximal normal subgroup of | D9×#15258 |
Past the SmallGroups library coverage — no SmallGroups id.