Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1294 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)(14,24,28,19)(15,29)(16,34,36,21)(17,22)(18,23)(20,32)(25,50,53,40)(26,41)(27,48,38,42)(30,57,56,43)(31,58,60,44)(33,49)(35,62,65,46)(37,47)(39,45)(51,54)(52,72)(55,67)(59,75)(61,71,64,69)(63,70)(66,73)(68,74);(12,14,17,28)(13,19,22,24)(15,30,32,56)(16,26,36,54)(18,38,37,27)(20,43,29,57)(21,41,34,51)(23,48,47,42)(25,39,53,33)(31,59,60,74)(35,63,65,55)(40,49,50,45)(44,68,58,75)(46,70,62,67)(52,64,73,61)(66,71,72,69);(12,15)(13,20)(14,25)(16,31)(17,32)(18,39)(19,40)(21,44)(22,29)(23,49)(24,50)(26,52)(27,56)(28,53)(30,38)(33,37)(34,58)(35,64)(36,60)(41,66)(42,57)(43,48)(45,47)(46,71)(51,72)(54,73)(55,74)(59,63)(61,65)(62,69)(67,75)(68,70);(12,16)(13,21)(14,26)(15,31)(17,36)(18,35)(19,41)(20,44)(22,34)(23,46)(24,51)(25,52)(27,55)(28,54)(29,58)(30,59)(32,60)(33,61)(37,65)(38,63)(39,64)(40,66)(42,67)(43,68)(45,69)(47,62)(48,70)(49,71)(50,72)(53,73)(56,74)(57,75)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17399);