Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#7258 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #102 |
| commutator | C2×C8 | C42×C11 |
| Frattini, cosocle | C23×C8 | C22×C11 |
| prime radical | C24×C11 | D8 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,20)(19,22)(21,23)(24,25)(26,29)(27,36)(28,32)(30,33)(31,34)(35,38)(37,39);(17,20,22,21)(25,29)(26,33)(27,34)(30,31)(32,38)(35,39)(36,37)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 246);