Finite Group DatabasebetaFinite Group Databasebeta| order | 26508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #27210411⋊C2 |
| unambiguous semidirect product | ((C47⋊D47)⋊C3)⋊C2 |
| Fitting, socle, Sylow | C472 ⋊ C2×D3 |
| derived, Hall | C472⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C472⋊C3 | C22 |
| Fitting, socle | C472 | C2×D3 |
| LCS | G ▷ C472⋊C3 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 141 |
Polycyclic presentation:
2^2,3,47^2|c^a=c^2,d^a=d^46e^45,c^b=c^2,d^b=de^2,e^b=e^46,d^c=d^20e^32,e^c=d^3e^26259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26508, 23);