Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#11492 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | C2×C22⋊C8 |
| prime radical | C11×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,17,15,16,18,19)(20,21,25,31,27,30,40,48,26,32,39,49,24,41,23,29)(22,33,36,47,35,28,34,44,37,46,50,43,42,45,38,51);(13,16)(14,18)(20,22)(21,28)(23,38)(24,42)(25,36)(26,37)(27,35)(29,47)(30,46)(31,44)(32,45)(33,41)(34,40)(39,50)(43,48)(49,51);(20,23,24,39,26,40,27,25)(21,29,41,49,32,48,30,31)(22,34,42,36,37,38,35,50)(28,43,33,44,45,47,46,51)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4480);