Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#11405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C42 |
| commutator | C4 | C2×C4×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#97 |
| prime radical | C23×C11 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(20,21,23,27,24,29,35,43,25,28,36,42,37,44,50,51)(22,30,32,46,33,39,48,41,31,45,34,49,47,26,38,40);(12,13,14,16,15,17,18,19)(20,22)(21,26,28,39)(23,34)(24,33)(25,31)(27,41,42,40)(29,30,44,45)(32,36)(35,38)(37,47)(43,49,51,46)(48,50);(22,31)(26,39)(30,45)(32,34)(33,47)(38,48)(40,41)(46,49)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4393);