Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61691 |
| 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 ◁ C11×#532 ◁ G | |
2046 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)(14,18)(15,17)(16,19)(20,21,25,31)(22,33,36,27)(23,29,38,45)(24,32,26,30)(28,40,44,37)(34,48,50,42)(35,43,39,46)(41,51,47,49);(12,14)(13,16)(15,19)(17,18)(20,22,25,36)(21,27,31,33)(23,34,38,50)(24,39,26,35)(28,41,44,47)(29,42,45,48)(30,46,32,43)(37,51,40,49);(20,23)(21,28)(22,34)(24,37)(25,38)(26,40)(27,41)(29,30)(31,44)(32,45)(33,47)(35,49)(36,50)(39,51)(42,46)(43,48);(14,19)(16,18)(20,23)(21,29)(22,34)(24,40)(25,38)(26,37)(27,42)(28,30)(31,45)(32,44)(33,48)(35,51)(36,50)(39,49)(41,46)(43,47);(13,17)(16,18)(20,24,25,26)(21,30,31,32)(22,35,36,39)(23,37,38,40)(27,43,33,46)(28,29,44,45)(34,49,50,51)(41,48,47,42)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54679);