Finite Group DatabasebetaFinite Group Databasebeta| order | 3249 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | C361 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C361 | C9 |
| Frattini, socle | C19 | #4296 |
| prime radical, cosocle | C361⋊C3 | C3 |
| LCS | G ▷ C361 | |
| UCS | C1 | |
9 conjugacy classes of subgroups.
| minimal degree | μ(G) = 361 |
| transitive degree | μt(G) = 361 |
Polycyclic presentation:
3^2,19^2|a^3=b,c^19=d^4,c^a=c^4d,d^a=d^4,c^b=c^7d^3,d^b=d^749 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊#15692425, C5×#15692425, C7×#15692425, … |
| maximal normal subgroup of | C5×#15692425, C7×#15692425, C11×#15692425 |
| maximal quotient of | C22⋊#15692425, C5×#15692425, C7×#15692425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3249, 4);