Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,31)(21,36)(22,42)(23,46)(24,29)(25,30)(26,34)(27,40)(28,43)(32,48)(33,61)(35,50)(37,52)(38,53)(39,55)(41,54)(44,56)(45,70)(47,51)(49,63)(57,62)(58,76)(59,73)(60,74)(64,66)(65,80)(67,69)(68,77)(71,75)(72,78)(79,81);(18,20,23,34,25,35,24,47)(19,26,29,31,30,51,46,50)(21,37,39,32,41,59,40,60)(22,33,43,62,45,63,44,71)(27,52,54,74,55,73,36,48)(28,49,42,57,56,61,70,75)(38,65,66,58,68,78,67,79)(53,76,69,80,77,81,64,72);(18,21)(19,27)(20,32)(22,38)(23,39)(24,40)(25,41)(26,48)(28,53)(29,54)(30,55)(31,52)(33,58)(34,59)(35,60)(36,46)(37,47)(42,69)(43,66)(44,67)(45,68)(49,72)(50,73)(51,74)(56,77)(57,76)(61,80)(62,78)(63,79)(64,70)(65,71)(75,81);(18,22,24,44,25,45,23,43)(19,28,46,70,30,56,29,42)(20,33,47,71,35,63,34,62)(21,38,40,67,41,68,39,66)(26,49,50,75,51,61,31,57)(27,53,36,64,55,77,54,69)(32,58,37,65,60,79,59,78)(48,72,73,81,74,80,52,76)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17284);