Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#24725 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16)(14,18,19,17)(20,21,26,31,24,29,25,30)(22,32,41,43,34,27,35,47)(23,36,40,28,38,46,39,45)(33,49,51,48,50,44,37,42);(13,16)(17,18)(20,22)(21,27)(23,37)(24,34)(25,35)(26,41)(28,44)(29,32)(30,43)(31,47)(33,40)(36,48)(38,51)(39,50)(42,46)(45,49);(20,23,24,38)(21,28,29,45)(22,33,34,50)(25,40,26,39)(27,42,32,48)(30,46,31,36)(35,51,41,37)(43,49,47,44);(12,14,15,19)(13,17,16,18)(21,29)(27,32)(28,45)(30,31)(36,46)(42,48)(43,47)(44,49)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17713);