Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33371 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×Q8 | C24×C11 |
| prime radical | C11×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×Q8×C11 ◁ C2×C11×H(5,𝔽2) ◁ G | |
1208 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)(12,13,18,23,19,24,15,21)(14,25,26,41,28,36,33,43)(16,22,30,40,17,31,29,39)(20,34,37,32,38,42,35,27);(12,14)(13,20)(15,26)(16,27)(17,32)(18,33)(19,28)(21,35)(22,36)(23,37)(24,38)(25,31)(29,34)(30,42)(39,41)(40,43);(12,15,19,18)(13,21,24,23)(14,26,28,33)(16,30,17,29)(20,35,38,37)(22,40,31,39)(25,41,36,43)(27,42,32,34);(12,16,19,17)(13,22,24,31)(14,27,28,32)(15,29,18,30)(20,36,38,25)(21,39,23,40)(26,34,33,42)(35,41,37,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26359);