Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#41 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
386 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)(12,13,18,23)(14,24,29,45)(15,30,34,67)(16,35,38,21)(17,39,42,66)(19,28,46,26)(20,47,50,33)(22,52,55,37)(25,58,31,68)(27,44,40,53)(32,70,36,54)(41,51,71,49)(43,72,48,63)(56,69,73,60)(57,62,74,64)(59,75,61,65);(12,14)(13,19)(15,31)(16,28)(17,40)(18,29)(20,48)(21,45)(22,53)(23,46)(24,35)(25,34)(26,38)(27,42)(30,65)(32,59)(33,60)(36,61)(37,62)(39,57)(41,63)(43,50)(44,55)(47,69)(49,73)(51,56)(52,64)(54,58)(66,74)(67,75)(68,70)(71,72);(12,15,18,34)(13,20,23,50)(14,25)(16,36,38,32)(17,41,42,71)(19,43)(21,51,35,49)(22,54,55,70)(24,56)(26,61)(27,63)(28,59)(29,31)(30,66,67,39)(33,52,47,37)(40,72)(44,58)(45,73)(46,48)(53,68)(57,75)(60,64)(62,69)(65,74)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6393);