Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #1055⋊C9 |
| derived, Sylow | C13 ⋊ C8×C9 |
| Hall | C13⋊C9 ⋊ C8 |
| Hall | #1055 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3×C4 | D13⋊C3 |
| commutator, hypocenter | C13 | C8×C9 |
| Fitting, cosocle | C3×C4×C13 | C2×C3 |
| socle, prime radical | C2×C3×C13 | C3×C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 936 |
Polycyclic presentation:
2,3,2,3,2,13|a^2=c,b^3=d,c^2=e,f^a=f^12,f^b=f^396 conjugacy classes — view the full character table.
| maximal subgroup of | #6092⋊C9, C8×D13⋊C9, #6094⋊C9, … |
| maximal normal subgroup of | #6092⋊C9, C8×D13⋊C9, #6094⋊C9, … |
| maximal quotient of | #6090⋊C9, C2×#1055⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 1);