Finite Group DatabasebetaFinite Group Databasebeta| order | 3300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#64470 |
| derived, Hall | C11×C52⋊C3 ⋊ C4 |
| Hall | C52×C11 ⋊ Dic3 |
| Hall | C52⋊C3 ⋊ Dic11 |
| Sylow | C52 ⋊ Dic33 |
| Sylow | C11 ⋊ #64470 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊#3874 |
| commutator, hypocenter | C11×C52⋊C3 | C4 |
| Fitting, socle | C2×C52×C11 | D3 |
| prime radical, cosocle | C2×C11×C52⋊C3 | C2 |
| LCS | G ▷ C11×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 660 |
Polycyclic presentation:
2,3,11,5^2,2|a^2=f,b^a=b^2,c^a=c^10,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^2136 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C11⋊#64470, C7⋊(C11⋊#64470), C121⋊#64470, … |
| maximal normal subgroup of | C7×C11⋊#64470, C11×C11⋊#64470 |
| maximal quotient of | C7×C11⋊#64470, C7⋊(C11⋊#64470), C121⋊#64470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3300, 48);