Finite Group DatabasebetaFinite Group Databasebeta| order | 25290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C32×C281 ⋊ C2×C5 |
| derived | C3×C281 ⋊ C2×C3×C5 |
| Hall | C32×C281⋊C5 ⋊ C2 |
| Hall | C3×D843 ⋊ C5 |
| Hall | C281⋊C5 ⋊ C3×D3 |
| Sylow | C281 ⋊ C3×C5×D3 |
| Sylow | C32 ⋊ D281⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(D281⋊C5) |
| commutator, cosocle, hypocenter | C3×C281 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C281 | C2×C5 |
| LCS | G ▷ C3×C281 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1686 |
297 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25290, 15);