Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60627 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
1998 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)(20,21,27,33)(22,29,36,42)(23,28,35,43)(24,30,38,45)(25,32,26,31)(34,44,48,51)(37,41,49,50)(39,47,40,46);(13,16)(17,19)(20,22,25,23,27,36,26,35)(21,28,31,29,33,43,32,42)(24,34,39,37,38,48,40,49)(30,41,46,44,45,50,47,51);(12,14,15,18)(13,17,16,19)(20,23,25,36,27,35,26,22)(21,29,31,43,33,42,32,28)(24,37,39,48,38,49,40,34)(30,44,46,50,45,51,47,41);(20,24)(21,30)(22,34)(23,37)(25,39)(26,40)(27,38)(28,41)(29,44)(31,46)(32,47)(33,45)(35,49)(36,48)(42,51)(43,50);(24,38)(30,45)(34,48)(37,49)(39,40)(41,50)(44,51)(46,47)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53615);