Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D52 |
| unambiguous semidirect product | C4⋊(C32×D13) |
| Fitting | C32×C4×C13 ⋊ C2 |
| Hall | C32×C13 ⋊ D4 |
| Sylow | C13 ⋊ C32×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C32 | C2×D13 |
| commutator, cosocle | C2×C13 | C22×C32 |
| Frattini | C2 | C2×C32×D13 |
| Fitting | C32×C4×C13 | C2 |
| socle | C2×C32×C13 | C22 |
| hypercenter | C32×C4 | D13 |
| hypocenter | C13 | C32×D4 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C32 ◁ C32×C4 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 468 |
261 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10597595, C3×#10597596, C3×#10597598, … |
| maximal normal subgroup of | C3×#10597595, C3×#10597596, C3×#10597598, … |
| maximal quotient of | C32×#6095, C32×D104, C32×Dic52, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 141);