Finite Group DatabasebetaFinite Group Databasebeta| order | 8796 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic733⋊C3 |
| derived, Sylow | C733 ⋊ C3×C4 |
| Hall | Dic733 ⋊ C3 |
| Hall | C733⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D733⋊C3 |
| commutator, hypocenter | C733 | C3×C4 |
| Fitting, socle | C2×C733 | C2×C3 |
| LCS | G ▷ C733 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,733,2|a^2=d,c^a=c^732,c^b=c^425256 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic733⋊C3, C3⋊(Dic733⋊C3) |
| maximal normal subgroup of | C3×Dic733⋊C3 |
| maximal quotient of | Dic733⋊C9, C3×Dic733⋊C3, C3⋊(Dic733⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8796, 2);