Finite Group DatabasebetaFinite Group Databasebeta| order | 25886 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C43 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C432 ⋊ C2×C7 |
| Hall | #27188202 ⋊ C2 |
| Hall | C43⋊D43 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C432 | C2×C7 |
| LCS | G ▷ C432 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 301 |
Polycyclic presentation:
2,7,43^2|c^a=c^42,d^a=d^42,c^b=c^41,d^b=d^21146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25886, 21);