Finite Group DatabasebetaFinite Group Databasebeta| order | 26508 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C47 |
| unambiguous semidirect product | (C47⋊Dic47)⋊C3 |
| derived, Sylow | C472 ⋊ C3×C4 |
| Hall | C47⋊Dic47 ⋊ C3 |
| Hall | C472⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C47⋊D47)⋊C3 |
| commutator, hypocenter | C472 | C3×C4 |
| Fitting, socle, cosocle | C2×C472 | C2×C3 |
| prime radical | C2×C472⋊C3 | C2 |
| LCS | G ▷ C472 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 564 |
Polycyclic presentation:
2,3,47^2,2|a^2=e,c^a=c^46,d^a=d^46,c^b=c^26d^22,d^b=c^30d^20748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26508, 13);