Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #64603⋊C3 |
| Hall | C3×C13⋊C3 ⋊ D4 |
| Sylow | C13 ⋊ C3×#67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D13⋊C3 |
| commutator, Fitting, socle, cosocle | C2×C3×C13 | C22×C3 |
| hypocenter | C3×C13 | C3×D4 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2^2,3,2,3,13|b^2=d,b^a=bd,f^a=f^12,e^b=e^2,f^c=f^939 conjugacy classes — view the full character table.
| maximal subgroup of | #10597732⋊C3, #10597737⋊C3, #10597739⋊C3, … |
| maximal normal subgroup of | #10597732⋊C3, #10597737⋊C3, #10597739⋊C3, … |
| maximal quotient of | #10597596⋊C3, #10597600⋊C3, #10597601⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 78);