Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3176 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
508 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(22,30)(23,34)(24,35)(26,37)(28,43)(29,42)(31,36)(32,47)(33,46)(38,41)(39,48)(40,51)(44,45)(49,50);(13,16)(17,19)(20,21,25,27)(22,26,33,39)(23,28,36,41)(24,29,35,42)(30,37,46,48)(31,38,34,43)(32,40,44,49)(45,50,47,51);(20,22,31,47,24,32,23,30,25,33,34,45,35,44,36,46)(21,26,38,51,29,40,28,37,27,39,43,50,42,49,41,48);(12,14,15,18)(13,17,16,19)(21,27)(26,39)(28,41)(29,42)(37,48)(38,43)(40,49)(50,51)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26731);