Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11858 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C11×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18,19,16)(15,17)(20,21,25,31,27,33,26,32)(22,34,37,49,39,50,38,45)(23,40,24,43,42,30,41,29)(28,44,46,36,48,35,47,51);(12,14)(13,16)(15,19)(17,18)(20,22)(21,28)(23,36)(24,44)(25,38)(26,37)(27,39)(29,34)(30,49)(31,47)(32,46)(33,48)(35,41)(40,45)(42,51)(43,50);(14,19)(16,18)(20,23,26,41,27,42,25,24)(21,29,31,40,33,43,32,30)(22,35,38,36,39,44,37,51)(28,45,46,34,48,49,47,50)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4882);