Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13460 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2058 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | C2×SD16 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22,24,38)(15,27)(16,31)(17,20)(18,25,23,39)(19,29)(21,33)(26,40,32,35)(28,34,42,37)(30,41)(36,43);(12,13)(14,23,24,18)(15,19)(16,21)(17,20)(22,25,38,39)(26,37,32,34)(27,29)(28,40,42,35)(30,36)(31,33)(41,43);(12,14,16,32,17,24,33,26)(13,18,21,37,20,23,31,34)(15,28,29,25,30,42,43,39)(19,35,27,22,36,40,41,38)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6448);