Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61091 |
| 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×#532 ◁ G | |
2650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,23,28)(18,29,33,45)(19,20,25,38)(21,27,22,26)(24,40,44,32)(30,31,34,47)(35,41,39,37)(36,46,42,43);(16,18,23,33)(17,24,28,44)(19,34,25,30)(20,36,38,42)(21,32,22,40)(26,29,27,45)(31,41,47,37)(35,46,39,43);(13,15)(16,19,23,25)(17,20,28,38)(18,30,33,34)(21,39,22,35)(24,42,44,36)(26,41,27,37)(29,31,45,47)(32,46,40,43);(16,20)(17,25)(18,31)(19,28)(21,37)(22,41)(23,38)(24,43)(26,39)(27,35)(29,34)(30,45)(32,42)(33,47)(36,40)(44,46);(16,21,23,22)(17,26,28,27)(18,32,33,40)(19,35,25,39)(20,37,38,41)(24,29,44,45)(30,43,34,46)(31,42,47,36)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54079);