Finite Group DatabasebetaFinite Group Databasebeta| order | 25180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D1259 |
| unambiguous semidirect product | C1259⋊(C22×C5) |
| unambiguous semidirect product | (C2×C1259)⋊(C2×C5) |
| Fitting, socle | C2×C5×C1259 ⋊ C2 |
| derived, Sylow | C1259 ⋊ C22×C5 |
| Hall | C5×C1259 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1259 |
| commutator, cosocle, hypocenter | C1259 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C1259 | C2 |
| LCS | G ▷ C1259 | |
| UCS | C1 ◁ C2×C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12590 |
6310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25180, 9);