Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×#1057 |
| derived, Sylow | C13 ⋊ C32×C8 |
| Hall | C32×C13 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #261 |
| commutator, hypocenter | C13 | C32×C8 |
| Frattini | C2 | C32×#261 |
| Fitting, socle, prime radical | C2×C32×C13 | C4 |
| cosocle | Dic13 | C2×C32 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 936 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#1057, C3×#10597691, C3×#10597692, … |
| maximal normal subgroup of | C3×D3×#1057, C3×#10597691, C3×#10597692, … |
| maximal quotient of | C32×#6092, C2×C32×#1057 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 97);