Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C16 · Schur multiplier (H2) = C23 |
| direct product | C11×#13558 |
| subgroup | G/H | |
|---|---|---|
| center | C11×C16 | C2×D4 |
| commutator | C4 | C22×C11×C16 |
| Frattini, cosocle | C2×C16 | C23×C11 |
| socle | C2×C11 | C2×C22⋊C16 |
| prime radical | C2×C11×#41 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C11×C16 ◁ C22×C11×C16 ◁ G | |
290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,23,17,24,35,50,18,25,36,51,38,52,63,72,19,21,37,44,39,45,64,68,15,22,32,47,33,48,60,70)(14,26,28,53,29,54,57,73,27,41,55,49,56,66,74,71,30,46,34,61,58,69,62,75,31,20,40,42,59,43,65,67);(12,14)(13,20)(15,31)(16,34)(17,29)(18,27)(19,30)(21,41)(22,46)(23,49)(24,43)(25,26)(28,37)(32,55)(33,59)(35,62)(36,40)(38,56)(39,58)(42,44)(45,66)(47,53)(48,69)(50,71)(51,61)(52,54)(57,64)(60,74)(63,65)(67,68)(70,73)(72,75);(13,21)(20,41)(22,25)(23,44)(24,45)(26,46)(42,49)(43,66)(47,51)(48,52)(50,68)(53,61)(54,69)(67,71)(70,72)(73,75)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6546);