Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | AGL(1,𝔽5)×ΓL(1,𝔽16)⋊D3 |
| Fitting, socle, derived, Hall | C32×C52 ⋊ C2×C42 |
| Sylow | C52 ⋊ C4×#624 |
| Sylow | C32 ⋊ C2×AGL(1,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C2×C42 |
| prime radical | D52×C3⋊D3 | C22 |
| cosocle | C32×D52 | C23 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
1009 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1009 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D32×AGL(1,𝔽5)2 |
| maximal normal subgroup of | D32×AGL(1,𝔽5)2 |
Past the SmallGroups library coverage — no SmallGroups id.