Finite Group DatabasebetaFinite Group Databasebeta| order | 1144 |
| isoclinism | isoclinic class of C11⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#1057 |
| derived, Hall | C11×C13 ⋊ C8 |
| Sylow | C13 ⋊ C11⋊C8 |
| Sylow | C11 ⋊ #1057 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊#261 |
| commutator, hypocenter | C11×C13 | C8 |
| Fitting, socle, prime radical | C2×C11×C13 | C4 |
| cosocle | C11×Dic13 | C2 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 1144 |
Polycyclic presentation:
2^3,11,13|a^2=b,b^2=c,d^a=d^10,e^a=e^8,e^b=e^1294 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1144, 6);