Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#22277 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C11×#376 ◁ G | |
826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,21)(19,22)(20,23)(24,25)(26,34)(27,38)(28,32)(29,43)(30,36)(31,41)(33,42)(35,49)(37,45)(39,53)(40,52)(44,54)(46,50)(47,55)(48,51);(12,14,15,13)(16,18,21,17)(19,22,20,23)(24,26)(25,30)(27,39)(28,36)(29,37)(31,46)(32,34)(33,45)(35,40)(38,49)(41,54)(42,51)(43,48)(44,47)(50,55)(52,53);(16,19,21,20)(17,22,18,23)(24,27,29,41,28,40,42,55)(25,31,33,38,32,47,43,52)(26,35,37,50,36,39,51,54)(30,44,45,53,34,46,48,49);(16,20,21,19)(17,22,18,23)(25,32)(26,36)(31,47)(33,43)(35,39)(37,51)(38,52)(50,54)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15265);