Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13417 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13418 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2041 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
422 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)(14,28)(15,35)(16,26)(17,42)(18,24)(19,23)(20,27)(21,30)(22,38)(25,44)(29,61)(31,48)(32,49)(33,51)(34,50)(36,47)(37,54)(39,59)(40,72)(41,56)(43,53)(45,55)(46,71)(52,64)(57,65)(58,67)(60,63)(62,73)(66,74)(68,70)(69,75);(12,14,20,34)(13,21,27,51)(15,36,40,66)(16,33,19,30)(17,32,44,65)(18,31,41,67)(22,52,55,61)(23,50,26,28)(24,57,56,49)(25,58,42,48)(29,43,64,39)(35,70,72,60)(37,63,46,68)(38,62,45,69)(47,71,74,54)(53,75,59,73);(12,15,16,37,20,40,19,46)(13,22,23,53,27,55,26,59)(14,29,30,62,34,64,33,69)(17,43,41,38,44,39,18,45)(21,47,28,60,51,74,50,70)(24,54,25,35,56,71,42,72)(31,66,65,63,67,36,32,68)(48,52,49,73,58,61,57,75)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6406);