Finite Group DatabasebetaFinite Group Databasebeta| order | 37510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C11×#13133723 |
| Fitting, socle, Hall | C2×C112×C31 ⋊ C5 |
| derived | C11×C31 ⋊ C2×C5×C11 |
| Hall | C112×C31 ⋊ C2×C5 |
| Hall | C2×C112 ⋊ ΓL(1,𝔽32) |
| Sylow | C112 ⋊ C2×ΓL(1,𝔽32) |
| Hall | C2×C31 ⋊ C11×C11⋊C5 |
| Sylow | C31 ⋊ C2×C11×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | #13133723 |
| commutator, cosocle, hypocenter | C11×C31 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C31 | C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C2×C11 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3410 |
1606 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37510, 160);