Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11893 |
| 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 | |
400 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)(20,21,24,30,26,32,25,31)(22,33,36,49,38,50,37,47)(23,39,41,29,43,48,42,28)(27,40,44,35,46,51,45,34);(12,14)(13,16)(15,19)(17,18)(20,22)(21,27)(23,40)(24,37)(25,36)(26,38)(28,47)(29,49)(30,45)(31,44)(32,46)(33,48)(34,41)(35,42)(39,50)(43,51);(14,19)(16,18)(20,23,24,41,26,43,25,42)(21,28,31,48,32,29,30,39)(22,34,36,40,38,35,37,51)(27,33,45,47,46,50,44,49)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4881);