Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33658 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,23)(14,19,25,41)(15,28,29,63)(16,32,37,68)(17,38,35,22)(20,44,45,30)(21,47,50,36)(24,52,53,62)(26,57,33,67)(27,60,56,43)(31,49,39,64)(34,46,66,51)(40,65,71,54)(42,70,48,59)(55,73,61,75)(58,72,69,74);(12,14)(13,19)(15,24)(16,33)(17,27)(18,25)(20,40)(21,48)(22,43)(23,41)(26,37)(28,62)(29,53)(30,65)(31,55)(32,67)(34,69)(35,56)(36,70)(38,60)(39,61)(42,50)(44,54)(45,71)(46,72)(47,59)(49,75)(51,74)(52,63)(57,68)(58,66)(64,73);(12,15,17,39,18,29,35,31)(13,20,22,51,23,45,38,46)(14,24,27,61,25,53,56,55)(16,34,36,44,37,66,47,30)(19,40,43,74,41,71,60,72)(21,49,32,63,50,64,68,28)(26,58,59,65,33,69,70,54)(42,73,57,62,48,75,67,52);(14,25)(19,41)(24,53)(26,33)(27,56)(40,71)(42,48)(43,60)(52,62)(54,65)(55,61)(57,67)(58,69)(59,70)(72,74)(73,75)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26646);