Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23943 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
1158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,22)(19,21)(20,23)(24,25,29,33)(26,30,35,44)(27,37,39,47)(28,40,42,32)(31,41,46,38)(34,48,49,55)(36,52,51,45)(43,53,54,50);(12,13)(14,15)(16,18,19,23)(17,20,21,22)(24,26)(25,30)(27,34)(28,36)(29,35)(31,43)(32,45)(33,44)(37,48)(38,50)(39,49)(40,52)(41,53)(42,51)(46,54)(47,55);(13,15)(24,27,29,39)(25,31,33,46)(26,34,35,49)(28,41,42,38)(30,43,44,54)(32,47,40,37)(36,53,51,50)(45,55,52,48);(17,21)(20,22)(26,35)(30,44)(34,49)(36,51)(43,54)(45,52)(48,55)(50,53)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16931);