Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
570 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)(20,21,27,32)(22,33,35,34)(23,39,29,25)(24,40,42,30)(26,43,41,31)(28,44,45,36)(37,47,50,48)(38,46,51,49);(13,16)(17,19)(20,22,25,37,26,38,24,36,27,35,39,50,41,51,42,44)(21,28,30,46,31,47,29,33,32,45,40,49,43,48,23,34);(12,14,15,18)(13,17,16,19)(20,23,24,31,41,40,25,21,27,29,42,43,26,30,39,32)(22,34,36,47,51,49,37,28,35,33,44,48,38,46,50,45);(22,35)(28,45)(33,34)(36,44)(37,50)(38,51)(46,49)(47,48)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26691);