Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | D9×#2846 |
| Fitting | C9×#2846 ⋊ C2 |
| Sylow | C9 ⋊ C2×#2846 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D9 |
| commutator, cosocle | C23×C9 | C25 |
| Frattini, socle | C23×C3 | C24×D3 |
| Fitting | C9×#2846 | C2 |
| hypercenter | #2846 | D9 |
| hypocenter | C9 | C2×#2846 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ #2846 | |
49335 conjugacy classes of subgroups; only the 1303 normal subgroups are shown.
This group has 49335 conjugacy classes of subgroups — too many to draw. Only its 1303 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×#23900 |
| maximal normal subgroup of | D9×#23900 |
Past the SmallGroups library coverage — no SmallGroups id.