Finite Group DatabasebetaFinite Group Databasebeta| order | 31100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C22×C5×C311⋊C5 |
| unambiguous semidirect product | (C22×C311)⋊C52 |
| unambiguous semidirect product | (C22×C5×C311)⋊C5 |
| Fitting, socle | C22×C5×C311 ⋊ C5 |
| derived, Sylow | C311 ⋊ C22×C52 |
| Hall | C22×C311 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | C311⋊C5 |
| commutator, cosocle, hypocenter | C311 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C311 | C5 |
| LCS | G ▷ C311 | |
| UCS | C1 ◁ C22×C5 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6220 |
1340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31100, 33);