Finite Group DatabasebetaFinite Group Databasebeta| order | 26508 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C47 |
| unambiguous semidirect product | #22579562⋊C3 |
| Fitting, socle, derived, Sylow | C472 ⋊ C3×C4 |
| Hall | #22579562 ⋊ C3 |
| Hall | C472⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C472 | C3×C4 |
| prime radical | (C47⋊D47)⋊C3 | C2 |
| cosocle | C47⋊D47 | C2×C3 |
| LCS | G ▷ C472 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 282 |
Polycyclic presentation:
2,3,2,47^2|a^2=c,d^a=d^19e^40,e^a=d^45e^28,d^b=d^43e^5,e^b=d^35e^3,d^c=d^46,e^c=e^46196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26508, 22);