Finite Group DatabasebetaFinite Group Databasebeta| order | 36652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C7⋊D1309 |
| unambiguous semidirect product | (C2×C7)⋊D1309 |
| unambiguous semidirect product | (C2×C11)⋊(C7⋊D119) |
| unambiguous semidirect product | (C2×C17)⋊(C7⋊D77) |
| Fitting, socle | C2×C72×C11×C17 ⋊ C2 |
| derived, Hall | C72×C11×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×D11 |
| Hall | C72×C11 ⋊ C2×D17 |
| Hall | C11×C17 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×D187 |
| Sylow | C17 ⋊ C2×C7⋊D77 |
| Sylow | C11 ⋊ C2×C7⋊D119 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊D1309 |
| commutator, cosocle, hypocenter | C72×C11×C17 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C11×C17 | C2 |
| LCS | G ▷ C72×C11×C17 | |
| UCS | C1 ◁ C2 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18326 |
9166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36652, 86);