Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9415 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#3184 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
442 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)(12,13,18,21)(14,17,20,16)(15,22)(19,23)(24,26)(25,27)(28,29)(30,37,38,41)(31,34,39,40)(32,35)(33,36)(42,43);(12,14,16,13,18,20,17,21)(15,22,24,19,25,27,23,26)(28,30,32,40,33,38,42,34)(29,31,35,41,36,39,43,37);(12,15)(13,19)(14,22)(16,24)(17,23)(18,25)(20,27)(21,26)(28,31)(29,34)(30,35)(32,41)(33,39)(36,40)(37,42)(38,43)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2405);