Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)(29,34)(30,37)(31,32)(36,41)(38,42)(39,40);(12,14,17,23)(13,18,20,27)(15,22,16,25)(19,26,24,21)(28,29,33,36)(30,38,40,42)(31,41,32,34)(35,37,43,39);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(28,30,33,40)(29,35,36,43)(31,37,32,39)(34,42,41,38)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3179);