Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61629 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61636 |
| 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×#525 ◁ G | |
2074 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)(22,27)(23,34)(24,29)(25,38)(26,30)(28,35)(31,46)(32,41)(33,42)(36,44)(37,43)(39,45)(40,49)(47,50)(48,51);(12,14)(13,16)(15,19)(17,18)(20,22,26,33)(21,27,30,42)(23,31,36,48)(24,37,25,32)(28,40,45,50)(29,43,38,41)(34,46,44,51)(35,49,39,47);(20,23)(21,28)(22,31)(24,35)(25,39)(26,36)(27,40)(29,44)(30,45)(32,47)(33,48)(34,38)(37,49)(41,46)(42,50)(43,51);(14,19)(16,18)(20,24,26,25)(21,29,30,38)(22,32,33,37)(23,35,36,39)(27,41,42,43)(28,44,45,34)(31,47,48,49)(40,46,50,51);(13,17)(16,18)(22,33)(27,42)(31,48)(32,37)(40,50)(41,43)(46,51)(47,49)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54624);