Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of A4×D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×D13⋊C3 |
| unambiguous semidirect product | (C13⋊C3)⋊(C2×A4) |
| unambiguous semidirect product | (C22×D13⋊C3)⋊C3 |
| unambiguous semidirect product | (A4×D13)⋊C3 |
| unambiguous semidirect product | (D13⋊A4)⋊C3 |
| Fitting, socle, derived | C22×C13 ⋊ C2×C32 |
| Hall | C22×D13 ⋊ C32 |
| Sylow | C13 ⋊ C2×C3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C13 | C2×C32 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 52 |
32 conjugacy classes — view the full character table.
| maximal subgroup of | A4⋊AGL(1,𝔽13), A4×AGL(1,𝔽13), S4×D13⋊C3, … |
| maximal normal subgroup of | A4⋊AGL(1,𝔽13), A4×AGL(1,𝔽13), S4×D13⋊C3, … |
| maximal quotient of | (C13⋊C3)⋊(#41⋊C3), SL(2,𝔽3)×D13⋊C3, A4×Dic13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 170);