Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D13⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D13⋊#157 |
| unambiguous semidirect product | #90866⋊C2 |
| Fitting, socle, derived, Hall | C32×C13 ⋊ C2×C4 |
| Sylow | C13 ⋊ C2×#157 |
| Sylow | C32 ⋊ C2×#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C13 | C2×C4 |
| prime radical | C3⋊D3×D13 | C2 |
| cosocle | C3⋊D39 | C22 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
Polycyclic presentation:
2^3,3^2,13|a^2=c,d^a=d^2e,e^a=de,f^a=f^8,d^b=d^2,e^b=e^2,d^c=d^2,e^c=e^2,f^c=f^1230 conjugacy classes — view the full character table.
| maximal subgroup of | #157×#261, D32⋊#261, #14273387, … |
| maximal normal subgroup of | #157×#261, D32⋊#261, #14273387, … |
| maximal quotient of | #14273021, #14273022, #14273023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 182);