Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24130 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#2535 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G | |
1184 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,22)(19,20)(21,23)(24,25)(26,33)(27,37)(28,32)(29,31)(30,36)(34,39)(35,38);(17,20)(21,22)(24,26,28,36)(25,30,32,33)(27,35,29,34)(31,38,37,39);(13,15)(26,34)(27,29)(30,38)(31,37)(33,39)(35,36);(16,18,19,23)(17,21,20,22)(24,27,28,29)(25,31,32,37)(26,35,36,34)(30,38,33,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17118);