Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C22×C9×D13 |
| Fitting | C22×C9×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C23×C9 |
| Hall | C9×C13 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C9 | D13 |
| commutator, hypocenter | C13 | C23×C9 |
| Frattini | C3 | C22×C3×D13 |
| Fitting | C22×C9×C13 | C2 |
| socle | C22×C3×C13 | C2×C3 |
| prime radical | C22×C3×D13 | C3 |
| cosocle | C3×C13 | C23×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C9 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 468 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14272422, C9×#6103, C9×C22⋊#261, … |
| maximal normal subgroup of | #14272422, C9×#6103, C9×C22⋊#261, … |
| maximal quotient of | C2×C9×Dic26, C2×C4×C9×D13, C2×C9×D52, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 68);