Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊(D13⋊C3)) |
| unambiguous semidirect product | D156⋊C3 |
| Fitting | C3×C4×C13 ⋊ C2×C3 |
| Hall | C3×C13⋊C3 ⋊ D4 |
| Sylow | C13 ⋊ C3×D12 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C3⋊(D13⋊C3) |
| commutator, socle, cosocle | C2×C3×C13 | C22×C3 |
| Fitting | C3×C4×C13 | C2×C3 |
| hypercenter | C4 | C3⋊(D13⋊C3) |
| hypocenter | C3×C13 | C3×D4 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2 ◁ C4 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2^2,3,2,3,13|b^2=d,b^a=bd,e^a=e^2,f^a=f^12,f^c=f^351 conjugacy classes — view the full character table.
| maximal subgroup of | #10597596⋊C3, #10597597⋊C3, #10597601⋊C3, … |
| maximal normal subgroup of | #10597596⋊C3, #10597597⋊C3, #10597601⋊C3, … |
| maximal quotient of | #10597658⋊C3, D312⋊C3, Dic156⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 94);