Finite Group DatabasebetaFinite Group Databasebeta| order | 25908 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic2159 |
| derived, Hall | C17×C127 ⋊ C3×C4 |
| Hall | C3×C17×C127 ⋊ C4 |
| Hall | C3×C127 ⋊ Dic17 |
| Sylow | C127 ⋊ C3×Dic17 |
| Hall | C3×C17 ⋊ Dic127 |
| Sylow | C17 ⋊ C3×Dic127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D2159 |
| commutator, hypocenter | C17×C127 | C3×C4 |
| Frattini | C2 | C3×D2159 |
| Fitting, socle, prime radical | C2×C3×C17×C127 | C2 |
| cosocle | C2×C17×C127 | C2×C3 |
| LCS | G ▷ C17×C127 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25908 |
6486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25908, 5);