Finite Group DatabasebetaFinite Group Databasebeta| order | 3332 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊#595 |
| Fitting, derived, Hall | C17×C49 ⋊ C4 |
| Sylow | C49 ⋊ #595 |
| Sylow | C17 ⋊ Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C17×C49 | C4 |
| Frattini | C7 | C7⋊#595 |
| socle | C7×C17 | Dic7 |
| prime radical | C7×D17 | D7 |
| cosocle | D17×C49 | C2 |
| LCS | G ▷ C17×C49 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 66 |
| transitive degree | μt(G) = 833 |
Polycyclic presentation:
2^2,7,17,7|a^2=b,c^7=e^6,c^a=c^6e,d^a=d^4,e^a=e^6,d^b=d^16248 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C49⋊#595, C49⋊#66775, C49⋊#66776, … |
| maximal normal subgroup of | C5×C49⋊#595, C11×C49⋊#595 |
| maximal quotient of | C5×C49⋊#595, C49⋊#66775, C49⋊#66776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3332, 7);