Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#92150⋊C25) |
| unambiguous semidirect product | (C3⋊#92150)⋊C25 |
| derived, Hall | C3×C112 ⋊ C4×C25 |
| Hall | C3×#15690027 ⋊ C4 |
| Hall | #15690027 ⋊ Dic3 |
| Hall | C3⋊#92150 ⋊ C25 |
| Sylow | C112 ⋊ Dic3×C25 |
| Sylow | C3 ⋊ #92150⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C3⋊(#92150⋊C5) |
| commutator, hypocenter | C3×C112 | C4×C25 |
| Fitting, socle | C3×C5×C112 | C4×C5 |
| prime radical, cosocle | C3×C5×C11⋊D11 | C2×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C5 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
Polycyclic presentation:
2,5,2,3,11^2,5|a^2=c,b^5=g,d^a=d^2,e^a=e^5f^7,f^a=ef^6,e^b=e^3,f^b=f^3,e^c=e^10,f^c=f^10240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 241);