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×#36573 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#127 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2082 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)(14,17)(15,16)(18,19)(20,21)(22,25)(23,26)(24,27)(28,29)(30,33)(31,32)(34,35);(12,13)(14,18)(15,16)(17,19)(20,22,23,27)(21,24,26,25)(29,32)(33,34);(13,16)(17,18)(20,21,23,26)(22,25,27,24)(28,29)(30,34)(31,32)(33,35);(12,13)(14,18)(15,16)(17,19)(20,21)(22,24)(23,26)(25,27)(28,30,31,35)(29,33,32,34);(12,14,15,19)(13,17,16,18)(20,22)(21,25)(23,27)(24,26)(28,29)(30,34)(31,32)(33,35)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29561);