Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13339 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 79 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,23,29)(18,30,35,65)(19,36,42,55)(20,43,48,61)(21,28,22,27)(24,49,53,32)(25,38,58,39)(26,46,62,47)(31,50,69,78)(33,59,34,64)(37,74,68,54)(40,60,41,73)(44,51,71,52)(45,56,76,57)(63,66,79,67)(70,72,75,77);(12,13)(14,15)(16,18,23,35)(17,24,29,53)(19,37,42,68)(20,44,48,71)(21,34,22,33)(25,54,58,74)(26,59,62,64)(27,52,28,51)(30,61,65,43)(31,41,69,40)(32,46,49,47)(36,72,55,77)(38,66,39,67)(45,75,76,70)(50,57,78,56)(60,79,73,63);(13,15)(16,19)(17,25)(18,31)(20,45)(21,41)(22,40)(23,42)(24,50)(26,60)(27,57)(28,56)(29,58)(30,63)(32,70)(33,68)(34,37)(35,69)(36,43)(38,46)(39,47)(44,67)(48,76)(49,75)(51,74)(52,54)(53,78)(55,61)(59,72)(62,73)(64,77)(65,79)(66,71)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6327);