Finite Group DatabasebetaFinite Group Databasebeta| order | 37860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D631⋊C5 |
| Fitting, socle | C2×C3×C631 ⋊ C2×C5 |
| derived, Sylow | C631 ⋊ C22×C3×C5 |
| Hall | C3×C631⋊C5 ⋊ C22 |
| Hall | C2×C3×D631 ⋊ C5 |
| Hall | C631⋊C5 ⋊ C22×C3 |
| Hall | C2×D631 ⋊ C3×C5 |
| Hall | C3×C631 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D631⋊C5 |
| commutator, cosocle, hypocenter | C631 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C631 | C2×C5 |
| LCS | G ▷ C631 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3786 |
438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37860, 28);