Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#72222577 |
| Fitting, socle | C2×C32×C52 ⋊ C22×C4 |
| derived, Hall | C32×C52 ⋊ C23×C4 |
| Sylow | C52 ⋊ C2×C4×D32 |
| Sylow | C32 ⋊ C22×D5⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72222577 |
| commutator, hypocenter | C32×C52 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C22×C4 |
| prime radical | C2×#14268487 | C2 |
| cosocle | C32×C5⋊D5 | C24 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
2244 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 2244 conjugacy classes of subgroups — too many to draw. Only its 247 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D32×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C2×D32×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.