Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2127 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33369 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×Q8 | C24×C11 |
| socle | C2×C11 | C22×#99 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G | |
1220 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)(12,13,17,22,18,23,15,20)(14,24,26,41,25,39,32,43)(16,29,28,40,31,21,33,38)(19,34,37,30,35,42,36,27);(12,14)(13,19)(15,26)(16,30)(17,32)(18,25)(20,36)(21,39)(22,37)(23,35)(24,29)(27,31)(28,34)(33,42)(38,43)(40,41);(14,25)(19,35)(24,39)(26,32)(27,30)(34,42)(36,37)(41,43);(12,15,18,17)(13,20,23,22)(14,26,25,32)(16,28,31,33)(19,36,35,37)(21,38,29,40)(24,41,39,43)(27,42,30,34)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26357);