Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C61⋊C3)⋊C25) |
| unambiguous semidirect product | (C22⋊(C61⋊C3))⋊C25 |
| unambiguous semidirect product | (C61⋊C25)⋊A4 |
| derived, Hall | C22×C61 ⋊ C3×C25 |
| Hall | C22×C61⋊C25 ⋊ C3 |
| Hall | C61⋊C25 ⋊ A4 |
| Hall | C22⋊(C61⋊C3) ⋊ C25 |
| Sylow | C61 ⋊ A4×C25 |
| Sylow | C22 ⋊ (C61⋊C3)⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C22⋊((C61⋊C3)⋊C5) |
| commutator, hypocenter | C22×C61 | C3×C25 |
| Fitting, socle, cosocle | C22×C5×C61 | C3×C5 |
| prime radical | C5×C22⋊(C61⋊C3) | C5 |
| LCS | G ▷ C22×C61 | |
| UCS | C1 ◁ C5 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6100 |
Polycyclic presentation:
3,5,2^2,61,5|b^5=f,c^a=d,d^a=cd,e^a=e^13,e^b=e^9180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 26);