Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C16 · Schur multiplier (H2) = C23 |
| direct product | C11×#13556 |
| subgroup | G/H | |
|---|---|---|
| center | C11×C16 | C22⋊C4 |
| commutator | C22 | C22×C11×C16 |
| Frattini, cosocle | C2×C16 | C23×C11 |
| socle | C2×C11 | C2×C22⋊C16 |
| prime radical | C2×C11×#41 | C8 |
| LCS | G ▷ C22 ▷ 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)(12,13,15,21,16,22,30,43,17,23,31,44,33,45,55,67,18,20,32,39,34,40,56,62,35,41,57,63,58,64,72,74)(14,24,26,42,27,46,50,65,28,47,51,66,52,68,70,75,25,19,29,36,48,37,53,59,49,38,54,60,69,61,71,73);(12,14)(13,19)(15,29)(16,27)(17,28)(18,25)(20,24)(21,42)(22,37)(23,38)(26,32)(30,53)(31,54)(33,52)(34,48)(35,49)(36,39)(40,46)(41,47)(43,65)(44,66)(45,61)(50,56)(51,57)(55,71)(58,69)(59,62)(60,63)(64,68)(67,75)(70,72)(73,74);(14,25)(19,24)(26,29)(27,48)(28,49)(36,42)(37,46)(38,47)(50,53)(51,54)(52,69)(59,65)(60,66)(61,68)(70,71)(73,75)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6544);