Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61484 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#529 ◁ G | |
1750 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)(13,16)(17,19)(20,21,24,28)(22,30,32,26)(23,34,35,43)(25,38,37,29)(27,39,42,36)(31,46,47,51)(33,41,49,45)(40,48,44,50);(12,13)(14,17)(15,16)(18,19)(20,22)(21,26)(23,31)(24,32)(25,33)(27,40)(28,30)(29,41)(34,51)(35,47)(36,48)(37,49)(38,45)(39,50)(42,44)(43,46);(20,23,24,35)(21,27,28,42)(22,31,32,47)(25,39,37,36)(26,40,30,44)(29,43,38,34)(33,50,49,48)(41,46,45,51);(13,16)(17,19)(22,32)(26,30)(31,47)(33,49)(40,44)(41,45)(46,51)(48,50);(12,14,15,18)(13,17,16,19)(22,32)(26,30)(31,47)(33,49)(40,44)(41,45)(46,51)(48,50)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54472);