Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5×C11 |
| unambiguous semidirect product | C11⋊(C11⋊(#1039⋊C3)) |
| derived, Hall | C52×C112 ⋊ C3×C4 |
| Hall | C11⋊(C11⋊#1039) ⋊ C3 |
| Hall | C112×C52⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ #1039⋊C3 |
| Hall | C52⋊C3 ⋊ C11⋊Dic11 |
| Sylow | C52 ⋊ C3×C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(C11⋊((C5⋊D5)⋊C3)) |
| commutator, hypocenter | C52×C112 | C3×C4 |
| Fitting, socle, cosocle | C2×C52×C112 | C2×C3 |
| prime radical | C2×C112×C52⋊C3 | C2 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 ◁ C2 | |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7260 |
Polycyclic presentation:
2,3,5^2,11^2,2|a^2=g,c^a=c^4,d^a=d^4,e^a=e^10,f^a=f^10,c^b=cd,d^b=c^2d^31340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 431);