Finite Group DatabasebetaFinite Group Databasebeta| order | 37026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C112 · Schur multiplier (H2) = C3×C11 |
| direct product | C32×C112×D17 |
| unambiguous semidirect product | C17⋊(C2×C32×C112) |
| Fitting, socle, Hall | C32×C112×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C32×C112 |
| Hall | C112×C17 ⋊ C2×C32 |
| Hall | C32×C17 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C112 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C32×C112 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112×C17 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C32×C112 | |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18513 |
10890 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37026, 52);