Finite Group DatabasebetaFinite Group Databasebeta| order | 31200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| general orthogonal | GO−(4,𝔽5) |
| direct product | C2×PΣL(2,𝔽25) |
| socle | C2×PSL(2,𝔽25) ⋊ C2 |
| derived | PSL(2,𝔽25) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2 | PΣL(2,𝔽25) |
| commutator, cosocle, hypocenter | PSL(2,𝔽25) | C22 |
| Frattini | C1 | G |
| socle | C2×PSL(2,𝔽25) | C2 |
| LCS | G ▷ PSL(2,𝔽25) | |
| UCS | C1 ◁ C2 | |
383 conjugacy classes of subgroups; only the 7 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 7 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
36 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.