Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| isoclinism | isoclinic class of C7⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#6092 |
| derived, Hall | C7×C13 ⋊ C16 |
| Sylow | C13 ⋊ C7⋊C16 |
| Sylow | C7 ⋊ #6092 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C7⋊#261 |
| commutator, hypocenter | C7×C13 | C16 |
| Fitting | C4×C7×C13 | C4 |
| socle, prime radical | C2×C7×C13 | C8 |
| cosocle | C7×#1055 | C2 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C4 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1456 |
Polycyclic presentation:
2^4,7,13|a^2=b,b^2=c,c^2=d,e^a=e^6,f^a=f^8,f^b=f^12124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 6);