Finite Group DatabasebetaFinite Group Databasebeta| order | 1144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C11×C13 ⋊ D4 |
| Sylow | C13 ⋊ C22⋊D11 |
| Sylow | C11 ⋊ D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D11×D13 |
| commutator, Fitting, socle, cosocle | C2×C11×C13 | C22 |
| hypocenter | C11×C13 | D4 |
| LCS | G ▷ C2×C11×C13 ▷ C11×C13 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 572 |
Polycyclic presentation:
2^3,11,13|b^2=c,b^a=bc,e^a=e^12,d^b=d^10109 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1144, 11);