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×#61492 |
| 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×#529 ◁ G | |
1770 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)(22,27)(23,35)(24,29)(25,39)(26,30)(28,37)(31,47)(32,42)(33,43)(34,49)(36,51)(38,45)(40,46)(41,48)(44,50);(12,13)(14,17)(15,16)(18,19)(20,22)(21,27)(23,36)(24,32)(25,34)(26,33)(28,44)(29,42)(30,43)(31,38)(35,51)(37,50)(39,49)(40,48)(41,46)(45,47);(20,23)(21,28)(22,31)(24,37)(25,40)(26,38)(27,41)(29,45)(30,46)(32,48)(33,36)(34,50)(35,39)(42,51)(43,44)(47,49);(13,16)(17,19)(20,24,26,25)(21,29,30,39)(22,32,33,34)(23,37,38,40)(27,42,43,49)(28,45,46,35)(31,48,36,50)(41,51,44,47);(12,14,15,18)(13,17,16,19)(22,33)(27,43)(31,36)(32,34)(41,44)(42,49)(47,51)(48,50)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54480);