Finite Group DatabasebetaFinite Group Databasebeta| order | 25914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D617⋊C7) |
| unambiguous semidirect product | D1851⋊C7 |
| unambiguous semidirect product | (C617⋊C7)⋊D3 |
| Fitting, socle, derived, Hall | C3×C617 ⋊ C2×C7 |
| Hall | C3×C617⋊C7 ⋊ C2 |
| Hall | C617⋊C7 ⋊ D3 |
| Hall | D1851 ⋊ C7 |
| Sylow | C617 ⋊ D3×C7 |
| Sylow | C3 ⋊ D617⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C617 | C2×C7 |
| LCS | G ▷ C3×C617 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1851 |
Polycyclic presentation:
2,3,7,617|b^a=b^2,d^a=d^616,d^c=d^420153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25914, 13);