Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60831 |
| 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 ◁ C4×C11×#41 ◁ 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)(22,31)(23,35)(24,30)(25,27)(26,39)(28,33)(29,37)(32,47)(34,43)(36,45)(38,44)(40,41)(42,48)(46,49)(50,51);(12,14,15,19)(13,16,17,18)(21,27)(28,41)(29,35)(30,39)(31,43)(42,51)(44,45)(46,47);(14,19)(16,18)(20,22,25,34)(21,28,27,41)(23,32,37,49)(24,33,26,40)(29,42,35,51)(30,43,39,31)(36,48,38,50)(44,46,45,47);(13,17)(16,18)(20,23)(21,29)(22,32)(24,38)(25,37)(26,36)(27,35)(28,42)(30,45)(31,46)(33,50)(34,49)(39,44)(40,48)(41,51)(43,47);(20,24,25,26)(21,30,27,39)(22,33,34,40)(23,36,37,38)(28,43,41,31)(29,44,35,45)(32,48,49,50)(42,46,51,47)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53819);