Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#8468 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C11×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20,22,17)(15,23,24,18)(16,19)(21,25)(26,27)(29,33,35,38)(34,42,43,41);(12,14)(13,17)(15,21)(16,22)(18,25)(19,20)(23,26)(24,27)(28,29)(30,34)(31,38)(32,35)(33,40)(36,41)(37,43)(39,42);(12,15,16,24)(13,18,19,23)(14,21,22,27)(17,25,20,26)(28,30,32,37)(29,34,35,43)(31,39,40,36)(33,41,38,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1456);