Finite Group DatabasebetaFinite Group Databasebeta| order | 37510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C11 |
| direct product | ΓL(1,𝔽32)×C11⋊D11 |
| Fitting, socle, derived, Hall | C112×C31 ⋊ C2×C5 |
| Hall | C112×ΓL(1,𝔽32) ⋊ C2 |
| Hall | C31×C11⋊D11 ⋊ C5 |
| Sylow | C112 ⋊ C2×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C5×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C31 | C2×C5 |
| LCS | G ▷ C112×C31 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3751 |
682 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37510, 154);