Finite Group DatabasebetaFinite Group Databasebeta| order | 33740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#11757210⋊C5 |
| unambiguous semidirect product | #11757210⋊(C5×C7) |
| unambiguous semidirect product | (C7×#11757210)⋊C5 |
| Fitting, socle, Hall | C7×C241 ⋊ C4×C5 |
| derived, Sylow | C241 ⋊ C4×C5×C7 |
| Hall | C7×C241⋊C5 ⋊ C4 |
| Hall | C7×#11757210 ⋊ C5 |
| Hall | C241⋊C5 ⋊ C4×C7 |
| Hall | #11757210 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11757210⋊C5 |
| commutator, hypocenter | C241 | C4×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C241 | C4×C5 |
| prime radical | C7×D241⋊C5 | C2 |
| cosocle | D241 | C2×C5×C7 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1687 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33740, 14);