Finite Group DatabasebetaFinite Group Databasebeta| order | 25886 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C432 ⋊ D7 |
| derived, Hall | #27188202 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #27188202 | C2 |
| Fitting, socle | C432 | D7 |
| LCS | G ▷ #27188202 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 86 |
Polycyclic presentation:
2,7,43^2|b^a=b^6,c^a=d,d^a=c,c^b=c^4,d^b=d^11200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25886, 8);