Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33705 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C23×C11 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
578 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)(20,21,27,33)(22,29,34,46)(23,28,37,43)(24,31,40,49)(25,30,41,48)(26,42,39,32)(35,47,50,45)(36,51,38,44);(13,16)(17,19)(20,22,25,35,26,36,40,37,27,34,41,50,39,38,24,23)(21,28,31,44,32,45,48,46,33,43,49,51,42,47,30,29);(12,14,15,18)(13,17,16,19)(20,23,24,38,39,50,41,34,27,37,40,36,26,35,25,22)(21,29,30,47,42,51,49,43,33,46,48,45,32,44,31,28);(22,34)(23,37)(28,43)(29,46)(35,50)(36,38)(44,51)(45,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26693);