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×#61693 |
| 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 | |
2014 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)(14,18)(15,17)(16,19)(20,21,25,31)(22,29,35,27)(23,36,38,46)(24,32,26,30)(28,40,44,37)(33,47,49,51)(34,42,39,45)(41,50,43,48);(12,14)(13,16)(15,19)(17,18)(20,22)(21,27)(23,33)(24,39)(25,35)(26,34)(28,41)(29,31)(30,45)(32,42)(36,51)(37,50)(38,49)(40,48)(43,44)(46,47);(20,23,25,38)(21,28,31,44)(22,33,35,49)(24,37,26,40)(27,41,29,43)(30,36,32,46)(34,48,39,50)(42,47,45,51);(14,19)(16,18)(20,22)(21,29)(23,33)(24,39)(25,35)(26,34)(27,31)(28,43)(30,42)(32,45)(36,47)(37,50)(38,49)(40,48)(41,44)(46,51);(13,17)(16,18)(20,24,25,26)(21,30,31,32)(22,34,35,39)(23,37,38,40)(27,42,29,45)(28,36,44,46)(33,48,49,50)(41,47,43,51)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54681);