Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of C3⋊(D13⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊(D13⋊A4) |
| unambiguous semidirect product | D39⋊A4 |
| unambiguous semidirect product | (C22⋊(C13⋊C3))⋊D3 |
| Fitting, socle, derived | C22×C3×C13 ⋊ C2×C3 |
| Sylow | C13 ⋊ D3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C3×C13 | C2×C3 |
| LCS | G ▷ C22×C3×C13 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2,3,2^2,3,13|e^a=e^2,f^a=f^12,c^b=d,d^b=cd,f^b=f^336 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D13⋊A4, C2×C3⋊(D13⋊A4), A4×C3⋊(D13⋊C3) |
| maximal normal subgroup of | D3×D13⋊A4, C2×C3⋊(D13⋊A4), A4×C3⋊(D13⋊C3) |
| maximal quotient of | C3⋊#10597713, C3⋊(D13⋊SL(2,𝔽3)), C3⋊(Dic13⋊A4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 202);