Finite Group DatabasebetaFinite Group Databasebeta| order | 36652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic1309 |
| unambiguous semidirect product | C11⋊(C7⋊Dic119) |
| derived, Hall | C72×C11×C17 ⋊ C4 |
| Hall | C72×C17 ⋊ Dic11 |
| Hall | C72×C11 ⋊ Dic17 |
| Hall | C11×C17 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic187 |
| Sylow | C17 ⋊ C7⋊Dic77 |
| Sylow | C11 ⋊ C7⋊Dic119 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊D1309 |
| commutator, hypocenter | C72×C11×C17 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C72×C11×C17 | C2 |
| LCS | G ▷ C72×C11×C17 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36652 |
Polycyclic presentation:
2,7^2,11,17,2|a^2=f,b^a=b^6,c^a=c^6,d^a=d^10,e^a=e^169166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36652, 29);