Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of A4⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | A4⋊(D13⋊C3) |
| unambiguous semidirect product | (C13⋊C3)⋊S4 |
| unambiguous semidirect product | (A4⋊D13)⋊C3 |
| Fitting, socle | C22×C13 ⋊ C3×D3 |
| derived | A4×C13 ⋊ C2×C3 |
| Sylow | C13 ⋊ C3×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C13 | C2×C3 |
| Fitting, socle | C22×C13 | C3×D3 |
| LCS | G ▷ A4×C13 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 52 |
Polycyclic presentation:
2,3^2,13,2^2|c^a=c^2,d^a=d^12,e^a=f,f^a=e,d^b=d^3,e^c=f,f^c=ef23 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D13⋊C3, C2×A4⋊(D13⋊C3), C3×A4⋊(D13⋊C3), … |
| maximal normal subgroup of | S4×D13⋊C3, C2×A4⋊(D13⋊C3), C3×A4⋊(D13⋊C3) |
| maximal quotient of | (C13⋊C3)⋊#226, (C13⋊C3)⋊GL(2,𝔽3), A4⋊(Dic13⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 169);