Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10253 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
504 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)(14,22)(15,19)(16,25)(17,21)(18,23)(20,26)(24,27)(28,29,33,37)(30,38,40,43)(31,36,32,35)(34,41,42,39);(12,14,17,15)(13,18,21,27)(16,24,26,23)(19,25,22,20)(28,30,33,40)(29,34,37,42)(31,41,32,39)(35,43,36,38);(12,15,17,14)(13,19,21,22)(16,23,26,24)(18,20,27,25)(29,35)(31,32)(34,38)(36,37)(39,41)(42,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3241);