Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C23×C3×D72 |
| Fitting, socle | C23×C3×C72 ⋊ C22 |
| derived, Sylow | C72 ⋊ C25×C3 |
| Hall | C3×C72 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | D72 |
| commutator, cosocle, hypocenter | C72 | C25×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C72 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C23×C3 | |
3394 conjugacy classes of subgroups; only the 1048 normal subgroups are shown.
This group has 3394 conjugacy classes of subgroups — too many to draw. Only its 1048 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
600 conjugacy classes. The character table is too large to display.
| maximal quotient of | C3×#72214319 |
Past the SmallGroups library coverage — no SmallGroups id.