Finite Group DatabasebetaFinite Group Databasebeta| order | 37510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C112 · Schur multiplier (H2) = C11 |
| direct product | C2×C112×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C2×C31)⋊(C5×C112) |
| Fitting, socle, Hall | C2×C112×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C2×C5×C112 |
| Hall | C112×C31 ⋊ C2×C5 |
| Hall | C2×C31 ⋊ C5×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C112 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C2×C5×C112 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C112 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7502 |
2662 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37510, 155);