Finite Group DatabasebetaFinite Group Databasebeta| order | 25756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊#10587739 |
| Fitting, socle, derived, Hall | C47×C137 ⋊ C4 |
| Sylow | C137 ⋊ Dic47 |
| Sylow | C47 ⋊ #10587739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C47×C137 | C4 |
| prime radical, cosocle | C47×D137 | C2 |
| LCS | G ▷ C47×C137 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6439 |
Polycyclic presentation:
2^2,47,137|a^2=b,c^a=c^46,d^a=d^100,d^b=d^1361648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25756, 7);