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×#33744 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
520 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)(23,32)(24,35)(26,37)(28,38)(29,41)(31,42)(33,49)(34,45)(36,48)(39,51)(40,46)(43,44)(47,50);(13,16)(17,19)(20,21)(22,31)(23,28)(24,29)(25,27)(26,34)(30,42)(32,38)(33,47)(35,41)(36,40)(37,45)(39,43)(44,51)(46,48)(49,50);(20,22,32,44,24,33,36,45,25,34,48,49,35,43,23,30)(21,26,38,50,29,39,40,42,27,31,46,51,41,47,28,37);(12,14,15,18)(13,17,16,19)(21,27)(26,31)(28,40)(29,41)(37,42)(38,46)(39,47)(50,51)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26732);