Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of A4×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×D13 |
| Fitting, socle | C22×C3×C13 ⋊ C2×C3 |
| derived | C22×C13 ⋊ C2×C32 |
| Hall | C22×D13 ⋊ C32 |
| Sylow | C13 ⋊ C2×C3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×D13 |
| commutator, cosocle, hypocenter | C22×C13 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C13 | C2×C3 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4⋊#261, C3⋊(A4⋊#261), C3×A4×#261, … |
| maximal normal subgroup of | C3×A4⋊#261, C3⋊(A4⋊#261), C3×A4×#261, … |
| maximal quotient of | C3×#10597710, C3×SL(2,𝔽3)×D13, C3×A4×Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 197);