Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33348 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33349 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C2×D4 | C24×C11 |
| prime radical | C11×#3486 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×Q8×C11 ◁ C2×C11×2−1+4 ◁ G | |
1190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,19)(15,20)(16,28,29,18)(17,21)(22,32)(23,37,38,30)(24,33)(25,34)(26,40,41,31)(27,35)(36,43,39,42);(13,18)(19,30)(20,31)(21,28)(32,42)(33,37)(34,43)(35,40);(12,14,17,24)(13,19,21,33)(15,25,27,22)(16,23,29,38)(18,30,28,37)(20,34,35,32)(26,39,41,36)(31,43,40,42);(12,15,17,27)(13,20,21,35)(14,22,24,25)(16,26,29,41)(18,31,28,40)(19,32,33,34)(23,36,38,39)(30,42,37,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26337);