Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60372 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3002 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
2024 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21)(22,27)(23,29)(24,30)(25,39)(26,31)(28,36)(32,41)(33,42)(34,49)(35,43)(37,44)(38,45)(40,46)(47,50)(48,51);(13,16)(17,19)(20,22,26,35)(21,27,31,43)(23,32,37,47)(24,33,25,34)(28,40,45,51)(29,41,44,50)(30,42,39,49)(36,46,38,48);(20,23)(21,28)(22,32)(24,36)(25,38)(26,37)(27,40)(29,39)(30,44)(31,45)(33,46)(34,48)(35,47)(41,49)(42,50)(43,51);(12,14,15,18)(13,17,16,19)(20,23)(21,29)(22,32)(24,38)(25,36)(26,37)(27,41)(28,39)(30,45)(31,44)(33,48)(34,46)(35,47)(40,49)(42,51)(43,50);(20,24,26,25)(21,30,31,39)(22,33,35,34)(23,36,37,38)(27,42,43,49)(28,44,45,29)(32,46,47,48)(40,50,51,41)671 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53574);