Finite Group DatabasebetaFinite Group Databasebeta| order | 37252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C67 · Schur multiplier (H2) = C2 |
| direct product | C2×C67×D139 |
| unambiguous semidirect product | C139⋊(C22×C67) |
| unambiguous semidirect product | (C2×C139)⋊(C2×C67) |
| Fitting, socle | C2×C67×C139 ⋊ C2 |
| derived, Sylow | C139 ⋊ C22×C67 |
| Hall | C67×C139 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C67 | D139 |
| commutator, cosocle, hypocenter | C139 | C22×C67 |
| Frattini | C1 | G |
| Fitting, socle | C2×C67×C139 | C2 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C67 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18626 |
9514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37252, 7);