Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#12613 |
| subgroup | G/H | |
|---|---|---|
| center | C11×C16 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | C8×C22⋊C4 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C11×C16 ◁ C22×C11×C16 ◁ G | |
410 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21,17,23,32,43,18,22,33,42,34,44,56,65)(14,24,27,46,28,47,52,68,26,19,35,37,51,38,58,61)(15,20,29,39,30,41,53,63,31,40,54,62,55,64,71,74)(25,45,49,66,50,67,70,75,48,36,57,59,69,60,72,73);(12,14)(13,19,22,24)(15,25)(16,27)(17,28)(18,26)(20,36,40,45)(21,37,42,46)(23,38,44,47)(29,49)(30,50)(31,48)(32,52)(33,35)(34,51)(39,59,62,66)(41,60,64,67)(43,61,65,68)(53,70)(54,57)(55,69)(56,58)(63,73,74,75)(71,72);(12,15,16,29,17,30,32,53,18,31,33,54,34,55,56,71)(13,20,21,39,23,41,43,63,22,40,42,62,44,64,65,74)(14,25,27,49,28,50,52,70,26,48,35,57,51,69,58,72)(19,36,37,59,38,60,61,73,24,45,46,66,47,67,68,75)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5601);