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×#60828 |
| 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 | |
2018 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)(22,30)(23,34)(24,26)(25,38)(27,33)(28,35)(29,37)(31,45)(32,43)(36,42)(39,40)(41,51)(44,46)(47,48)(49,50);(12,14,15,19)(13,16,17,18)(21,26)(27,40)(28,34)(29,38)(30,43)(41,48)(42,49)(44,45);(14,19)(16,18)(20,22,24,32)(21,27,26,40)(23,31,35,46)(25,39,37,33)(28,41,34,48)(29,43,38,30)(36,51,50,47)(42,45,49,44);(13,17)(16,18)(20,23)(21,28)(22,31)(24,35)(25,36)(26,34)(27,41)(29,42)(30,44)(32,46)(33,47)(37,50)(38,49)(39,51)(40,48)(43,45);(23,35)(28,34)(31,46)(36,50)(41,48)(42,49)(44,45)(47,51)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53816);