Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C32×Q8×C13 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C32×C13 | C22 |
| commutator, Frattini, cosocle | C2 | C22×C32×C13 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C13 ◁ G | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 936 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(7,8,9,10)(11,14,13,12)(15,16,17,18,19,20,21,22,23,24,25,26,27);(4,5,6)(7,11,9,13)(8,12,10,14)585 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 166);