Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33671 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
554 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)(14,17)(15,16)(18,19)(20,21)(22,32)(23,29)(24,30)(25,28)(26,40)(27,34)(31,39)(33,47)(35,46)(36,42)(37,44)(38,45)(41,50)(43,49)(48,51);(13,16)(17,19)(20,22,24,34)(21,27,30,32)(23,33,26,36)(25,35,38,50)(28,41,45,46)(29,42,40,47)(31,43,44,48)(37,49,39,51);(21,28)(23,26)(25,39)(27,41)(29,31)(30,45)(32,46)(33,36)(35,51)(37,38)(40,44)(42,43)(47,48)(49,50);(12,14,15,18)(13,17,16,19)(20,23,24,26)(21,29,30,40)(22,33,34,36)(25,37,38,39)(27,42,32,47)(28,44,45,31)(35,49,50,51)(41,48,46,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26659);