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×#36587 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C11×#2856 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2040 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)(12,13)(14,19)(15,17)(16,18)(20,21,25,23)(22,26,24,27)(28,29)(30,32)(31,34)(33,35);(12,14)(13,17)(15,16)(18,19)(20,21,25,23)(22,27,24,26)(28,30,33,34)(29,31,35,32);(12,13,16,18)(14,19,15,17)(20,22,25,24)(21,26,23,27)(28,31,33,32)(29,34,35,30);(12,13)(14,17)(15,19)(16,18)(20,23,25,21)(22,26,24,27)(28,29)(30,31)(32,34)(33,35);(12,15,16,14)(13,17,18,19)(20,24,25,22)(21,27,23,26)(28,32,33,31)(29,30,35,34)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29575);