Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C9×C13 ⋊ D4 |
| Sylow | C13 ⋊ D36 |
| Sylow | C9 ⋊ C22⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×D13 |
| commutator, Fitting, cosocle | C2×C9×C13 | C22 |
| Frattini | C2×C3 | D3×D13 |
| socle | C2×C3×C13 | C2×D3 |
| hypocenter | C9×C13 | D4 |
| LCS | G ▷ C2×C9×C13 ▷ C9×C13 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 468 |
Polycyclic presentation:
2^3,3,13,3|a^2=c,d^3=f,b^a=bc,e^a=e^12,d^b=d^2f^2,f^b=f^293 conjugacy classes — view the full character table.
| maximal subgroup of | #14272550, #14272551, #14272556, … |
| maximal normal subgroup of | #14272550, #14272551, #14272556, … |
| maximal quotient of | #14272402, #14272403, #14272404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 18);