Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊(D61⋊C5) |
| unambiguous semidirect product | (C3⋊(D61⋊C5))⋊D5 |
| unambiguous semidirect product | (C5⋊(D61⋊C5))⋊D3 |
| unambiguous semidirect product | (D15⋊D61)⋊C5 |
| Fitting, socle, derived | C3×C5×C61 ⋊ C22×C5 |
| Hall | C3×C5×C61⋊C5 ⋊ C22 |
| Hall | C5×C61⋊C5 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×C5×D5 |
| Sylow | C61 ⋊ C5×D3×D5 |
| Sylow | C3 ⋊ D5×D61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C61 | C22×C5 |
| LCS | G ▷ C3×C5×C61 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 915 |
Polycyclic presentation:
2^2,5,3,5,61|e^a=e^4,f^a=f^60,d^b=d^2,e^b=e^4,f^c=f^9114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 139);