Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33495 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C24 |
| commutator | C22 | C23×C8×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C23×C8 |
| prime radical | C11×#532 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
564 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)(14,18)(15,17)(16,19)(20,21,24,29,25,30,36,44,23,28,34,42,35,43,47,51)(22,27,32,40,33,41,46,50,31,26,37,38,45,39,48,49);(12,14)(13,16)(15,19)(17,18)(20,22)(21,26)(23,31)(24,32)(25,33)(27,28)(29,38)(30,39)(34,37)(35,45)(36,46)(40,42)(41,43)(44,49)(47,48)(50,51);(14,19)(16,18)(20,22)(21,27)(23,31)(24,32)(25,33)(26,28)(29,40)(30,41)(34,37)(35,45)(36,46)(38,42)(39,43)(44,50)(47,48)(49,51);(13,17)(16,18)(21,28)(22,31)(29,42)(30,43)(32,37)(33,45)(44,51)(46,48)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26483);