Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9415 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9416 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
380 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21,22,25)(15,18,23,24)(16,19)(17,20)(26,27)(28,29)(30,39)(31,43,46,53)(32,47)(33,37)(34,38)(35,41)(36,45,52,44)(40,55,57,49)(42,50)(48,51)(54,56,59,58);(12,14,16,24,17,22,26,18)(13,15,19,25,20,23,27,21)(28,30,32,41,34,42,33,48)(29,35,37,39,38,51,47,50)(31,40,45,58,46,57,44,56)(36,49,53,54,52,55,43,59);(12,15)(13,18)(14,19)(16,25)(17,23)(20,24)(21,26)(22,27)(28,31,34,46)(29,36,38,52)(30,40,42,57)(32,45,33,44)(35,49,51,55)(37,53,47,43)(39,54,50,59)(41,58,48,56)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2404);