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×#36607 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2524 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,17)(14,15,18,19)(20,21,24,23)(22,25,27,26)(28,29,33,31)(30,34,32,35);(12,13)(14,15)(16,17)(18,19)(20,22)(21,25)(23,26)(24,27)(28,29,33,31)(30,35,32,34);(13,17)(14,18)(20,22,24,27)(21,26,23,25)(28,30,33,32)(29,34,31,35);(12,14)(13,15)(16,18)(17,19)(20,22)(21,25)(23,26)(24,27)(28,31,33,29)(30,34,32,35);(12,15)(13,18)(14,17)(16,19)(20,23,24,21)(22,25,27,26)(28,32,33,30)(29,35,31,34)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29595);