Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D32⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D32⋊D13 |
| Fitting, socle, Hall | C32×C13 ⋊ D4 |
| Sylow | C13 ⋊ GO+(4,𝔽2) |
| Sylow | C32 ⋊ C22⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C13×C3⋊D3 | C22 |
| Fitting, socle, hypocenter | C32×C13 | D4 |
| LCS | G ▷ C13×C3⋊D3 ▷ C32×C13 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
Polycyclic presentation:
2^3,3^2,13|b^a=bc,d^a=d^2,e^a=d^2e,f^a=f^12,d^b=d^2e^2,d^c=d^2,e^c=e^263 conjugacy classes — view the full character table.
| maximal subgroup of | D13×GO+(4,𝔽2), C2×D32⋊D13 |
| maximal normal subgroup of | D13×GO+(4,𝔽2), C2×D32⋊D13 |
| maximal quotient of | #14273040, D32⋊Dic13, #14273042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 185);