Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#36533 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C11×#2456 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(20,21)(22,24)(23,25)(26,27)(28,29,33,35)(30,32,34,31);(12,13)(14,18)(15,19)(16,17)(20,21)(22,26)(23,25)(24,27)(28,30,33,34)(29,31,35,32);(13,17)(14,19)(20,21,23,25)(22,24,27,26)(28,29)(30,31)(32,34)(33,35);(12,14,16,19)(13,18,17,15)(20,21)(22,26)(23,25)(24,27)(28,31,33,32)(29,30,35,34);(12,15,16,18)(13,14,17,19)(20,22,23,27)(21,24,25,26)(28,32,33,31)(29,34,35,30)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29521);