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×#36604 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C11×#2543 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1888 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)(12,13,17,15)(14,18,16,19)(20,21,24,23)(22,26,27,25)(29,34)(30,35);(12,13,17,15)(14,19,16,18)(20,22,24,27)(21,25,23,26)(28,29)(30,31)(32,35)(33,34);(12,14,17,16)(13,18,15,19)(20,22)(21,26)(23,25)(24,27)(28,30,33,35)(29,31,34,32);(12,15,17,13)(14,18,16,19)(20,23,24,21)(22,26,27,25)(28,31,33,32)(29,30,34,35);(12,16,17,14)(13,19,15,18)(20,22)(21,26)(23,25)(24,27)(28,32,33,31)(29,35,34,30)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29592);