Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19014 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19049 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3561 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,23)(14,24,15,26)(16,21,17,22)(19,27,20,25)(28,29,33,31)(30,36,38,43)(32,40,42,35)(34,41,37,39);(12,14,18,15)(13,19,23,20)(16,27,17,25)(21,24,22,26)(28,30,33,38)(29,34,31,37)(32,41,42,39)(35,43,40,36);(12,15,18,14)(13,20,23,19)(16,27,17,25)(21,24,22,26)(28,31,33,29)(30,37,38,34)(32,35,42,40)(36,41,43,39);(12,16,18,17)(13,21,23,22)(14,25,15,27)(19,26,20,24)(30,38)(34,37)(36,43)(39,41)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12037);