Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5⋊(D61⋊C5) |
| unambiguous semidirect product | (C2×C5)⋊(C3×D61⋊C5) |
| unambiguous semidirect product | (C2×C3×D305)⋊C5 |
| Fitting, socle | C2×C3×C5×C61 ⋊ C2×C5 |
| derived | C5×C61 ⋊ C22×C3×C5 |
| Hall | C3×C5×C61⋊C5 ⋊ C22 |
| Hall | C5×C61⋊C5 ⋊ C22×C3 |
| Hall | C3×C61 ⋊ C2×C5×D5 |
| Sylow | C61 ⋊ C2×C3×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊(D61⋊C5) |
| commutator, cosocle, hypocenter | C5×C61 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C61 | C2×C5 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C2×C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1830 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 190);