Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10500 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#10505 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,18)(17,19)(20,21,25,29)(22,27,31,35)(23,32,30,26)(24,34,33,28);(14,19)(16,17)(20,22,25,31)(21,26,29,32)(23,33,30,24)(27,28,35,34);(13,16)(14,19)(17,18)(20,23,24,22,25,30,33,31)(21,27,28,32,29,35,34,26)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3493);