Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×C9×C13 ⋊ C2 |
| Hall | C9×C13 ⋊ D4 |
| Sylow | C13 ⋊ #611 |
| Sylow | C9 ⋊ C22⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D117 |
| commutator, cosocle | C2×C9×C13 | C22 |
| Frattini | C2×C3 | C2×D39 |
| Fitting | C22×C9×C13 | C2 |
| socle | C2×C3×C13 | C2×D3 |
| hypercenter | C22 | D117 |
| hypocenter | C9×C13 | D4 |
| LCS | G ▷ C2×C9×C13 ▷ C9×C13 | |
| UCS | C1 ◁ C2 ◁ C22 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 468 |
Polycyclic presentation:
2^3,3,13,3|d^3=f,b^a=bc,d^a=d^2f^2,e^a=e^12,f^a=f^2237 conjugacy classes — view the full character table.
| maximal subgroup of | #14272565, #14272569, D13×#611, … |
| maximal normal subgroup of | #14272565, #14272569, D13×#611, … |
| maximal quotient of | #14272473, #14272475, #14272476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 41);