Finite Group DatabasebetaFinite Group Databasebeta| order | 4960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | #41×D31⋊C5 |
| Fitting | #41×C31 ⋊ C2×C5 |
| Hall | #41×D31 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×#41 |
| Sylow | C31 ⋊ C2×C5×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D31⋊C5 |
| commutator, socle, cosocle | C2×C31 | C24×C5 |
| Frattini | C2 | C23×D31⋊C5 |
| Fitting | #41×C31 | C2×C5 |
| hypercenter | #41 | D31⋊C5 |
| hypocenter | C31 | C2×C5×#41 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C4 ◁ #41 | |
328 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 248 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | H(5,𝔽2)×D31⋊C5 |
| maximal normal subgroup of | H(5,𝔽2)×D31⋊C5 |
Past the SmallGroups library coverage — no SmallGroups id.