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×#61627 |
| 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 | |
2050 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)(23,35)(24,29)(25,38)(26,30)(28,36)(31,46)(32,41)(33,42)(34,43)(37,44)(39,45)(40,47)(48,51)(49,50);(12,14)(13,16)(15,19)(17,18)(20,22)(21,27)(23,31)(24,32)(25,33)(26,34)(28,40)(29,41)(30,43)(35,46)(36,47)(37,49)(38,42)(39,48)(44,50)(45,51);(20,23,26,37)(21,28,30,45)(22,31,34,49)(24,36,25,39)(27,40,43,51)(29,44,38,35)(32,47,33,48)(41,50,42,46);(14,19)(16,18)(20,24,26,25)(21,29,30,38)(22,32,34,33)(23,36,37,39)(27,41,43,42)(28,44,45,35)(31,47,49,48)(40,50,51,46);(13,17)(16,18)(20,24,26,25)(21,29,30,38)(22,33,34,32)(23,36,37,39)(27,42,43,41)(28,44,45,35)(31,48,49,47)(40,46,51,50)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54615);