Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61643 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61676 |
| 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×#532 ◁ G | |
2024 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)(22,29)(23,36)(24,32)(25,31)(26,30)(27,35)(28,38)(33,48)(34,43)(37,51)(39,47)(40,46)(41,45)(42,49)(44,50);(12,14)(13,16)(15,19)(17,18)(20,22,25,35)(21,27,31,29)(23,37,39,33)(24,40,26,34)(28,44,45,42)(30,46,32,43)(36,48,47,51)(38,49,41,50);(20,23,25,39)(21,28,31,45)(22,33,35,37)(24,38,26,41)(27,42,29,44)(30,36,32,47)(34,49,40,50)(43,48,46,51);(14,19)(16,18)(20,22)(21,29)(23,33)(24,40)(25,35)(26,34)(27,31)(28,44)(30,43)(32,46)(36,48)(37,39)(38,50)(41,49)(42,45)(47,51);(13,17)(16,18)(20,24,25,26)(21,30,31,32)(22,34,35,40)(23,38,39,41)(27,43,29,46)(28,36,45,47)(33,49,37,50)(42,48,44,51)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54664);