Finite Group DatabasebetaFinite Group Databasebeta| order | 36652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C7⋊D7)⋊D187 |
| Fitting, socle, derived, Hall | C72×C11×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×D11 |
| Hall | C72×C11 ⋊ C2×D17 |
| Hall | C11×C17 ⋊ D72 |
| Sylow | C72 ⋊ C2×D187 |
| Sylow | C17 ⋊ (C7⋊D7)⋊D11 |
| Sylow | C11 ⋊ (C7⋊D7)⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11×C17 | C22 |
| LCS | G ▷ C72×C11×C17 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2618 |
Polycyclic presentation:
2^2,7^2,11,17|c^a=c^6,e^a=e^10,f^a=f^16,c^b=c^6,d^b=d^62443 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36652, 67);