Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#13216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1961 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
434 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)(14,25)(15,31,35,64)(16,37)(17,23)(18,41)(19,24)(20,28)(21,34,49,36)(22,38)(26,50)(27,57,59,73)(29,52)(30,54)(32,65,68,51)(33,69,70,48)(39,42)(40,53)(43,67,62,74)(44,60)(45,55)(46,61)(47,58,72,75)(56,71,66,63);(12,14,26,55,18,29,16,28,19,30,38,60,17,40,39,61)(13,20,42,52,23,45,22,25,24,46,37,53,41,44,50,54)(15,32,66,75,36,59,70,74,35,68,56,58,34,27,33,67)(21,47,63,65,31,62,69,57,49,72,71,51,64,43,48,73);(12,15)(13,21,24,49)(14,27,30,59)(16,33)(17,34)(18,36)(19,35)(20,43)(22,48,50,69)(23,31,41,64)(25,51)(26,56)(28,58,61,75)(29,32,40,68)(37,63,42,71)(38,66)(39,70)(44,72)(45,47)(46,62)(52,57)(53,73)(54,65)(55,74,60,67)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6204);