Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18262 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3534 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1012 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)(12,13,17,15)(14,22,26,38)(16,29,31,41)(18,20,33,27)(19,34,23,24)(21,36,28,32)(25,37,40,42)(30,35,43,39);(12,14)(13,19)(15,23)(16,30)(17,26)(18,25)(20,35)(21,37)(22,29)(24,32)(27,39)(28,42)(31,43)(33,40)(34,36)(38,41);(12,15)(13,17)(14,23)(16,21)(18,27)(19,26)(20,33)(22,24)(25,39)(28,31)(29,32)(30,37)(34,38)(35,40)(36,41)(42,43);(13,20)(15,27)(19,35)(21,29)(22,37)(23,39)(28,41)(38,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11250);