Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C25×C61 ⋊ C22×C3 |
| Hall | D25×D61 ⋊ C3 |
| Hall | C25×C61⋊C3 ⋊ C22 |
| Hall | C61⋊C3 ⋊ C2×D25 |
| Sylow | C61 ⋊ C2×C3×D25 |
| Sylow | C25 ⋊ C2×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C61 | C22×C3 |
| Frattini | C5 | D5×D61⋊C3 |
| socle | C5×C61 | C2×C3×D5 |
| LCS | G ▷ C25×C61 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1525 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 34);