Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5×C11 |
| unambiguous semidirect product | C11⋊(C11⋊#64480) |
| Fitting, socle, Hall | C52×C112 ⋊ Dic3 |
| derived, Hall | C112×C52⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ #64480 |
| Hall | C52⋊C3 ⋊ C11⋊Dic11 |
| Sylow | C52 ⋊ C3⋊(C11⋊Dic11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C112×C52⋊C3 | C4 |
| Fitting, socle | C52×C112 | Dic3 |
| prime radical, cosocle | C112×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C112×C52⋊C3 | |
| UCS | C1 | |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1815 |
Polycyclic presentation:
2^2,3,11^2,5^2|a^2=b,c^a=c^2,d^a=d^10,e^a=e^10,f^a=fg^4,g^a=f^2g^4,f^b=f^4,g^b=g^4,f^c=f^3g^2,g^c=fg608 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 703);