Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33540 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
1078 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)(14,26)(15,31)(16,35)(17,25)(18,24)(19,22)(20,28)(21,33)(23,38)(27,54)(29,60)(30,53)(32,63)(34,50)(36,51)(37,47)(39,49)(40,45)(41,48)(42,69)(43,59)(44,67)(46,66)(52,56)(55,61)(57,74)(58,72)(62,65)(64,70)(68,73)(71,75);(12,14,19,30)(13,20,22,43)(15,27,34,58)(16,36,39,67)(17,29,18,41)(21,42,45,70)(23,48,47,60)(24,44,25,51)(26,49,53,35)(28,37,59,38)(31,61,50,71)(32,64,66,69)(33,56,40,57)(46,72,63,54)(52,73,74,62)(55,68,75,65);(12,15)(13,21)(14,27)(16,32)(17,40)(18,33)(19,34)(20,42)(22,45)(23,46)(24,50)(25,31)(26,52)(28,55)(29,57)(30,58)(35,62)(36,64)(37,68)(38,65)(39,66)(41,56)(43,70)(44,71)(47,63)(48,72)(49,73)(51,61)(53,74)(54,60)(59,75)(67,69);(13,22)(20,43)(21,45)(23,47)(24,25)(26,53)(31,50)(35,49)(42,70)(44,51)(46,63)(48,60)(52,74)(54,72)(61,71)(62,73)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26528);