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×#60598 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
2010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
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)(28,35)(32,41)(33,42)(34,44)(36,45)(37,43)(38,46)(40,48)(47,50)(49,51);(13,16)(17,19)(20,22,26,34)(21,27,31,44)(23,32,36,49)(24,37,25,33)(28,40,46,50)(29,41,45,51)(30,43,39,42)(35,48,38,47);(20,23)(21,28)(22,32)(24,35)(25,38)(26,36)(27,40)(29,39)(30,45)(31,46)(33,47)(34,49)(37,48)(41,42)(43,51)(44,50);(12,14,15,18)(13,17,16,19)(20,23)(21,29)(22,32)(24,38)(25,35)(26,36)(27,41)(28,39)(30,46)(31,45)(33,48)(34,49)(37,47)(40,42)(43,50)(44,51);(20,24,26,25)(21,30,31,39)(22,33,34,37)(23,35,36,38)(27,42,44,43)(28,45,46,29)(32,47,49,48)(40,41,50,51)671 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53586);