Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C27 |
| direct product | D5×#87588 |
| Fitting, socle | C26×C5 ⋊ C2×D3 |
| derived | C5×C22⋊(C22⋊A4) ⋊ C22 |
| Sylow | C5 ⋊ C2×#87588 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C22⋊(C22⋊A4) | C22 |
| Fitting, socle | C26×C5 | C2×D3 |
| LCS | G ▷ C5×C22⋊(C22⋊A4) | |
| UCS | C1 | |
13690 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 13690 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#87588 |
| maximal normal subgroup of | AGL(1,𝔽5)×#87588 |
| maximal quotient of | D5×#11715850 |
Past the SmallGroups library coverage — no SmallGroups id.