Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13392 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #2033 |
| prime radical | C17×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,30)(21,36)(22,42)(23,45)(24,29)(25,32)(26,39)(27,44)(28,43)(31,61)(33,50)(34,51)(35,52)(37,71)(38,69)(40,70)(41,57)(46,56)(47,54)(48,75)(49,77)(53,74)(55,73)(58,76)(59,63)(60,66)(62,78)(64,80)(65,79)(67,68)(72,81);(18,20)(19,25)(21,37)(22,34)(23,46)(24,35)(26,49)(27,52)(28,56)(29,51)(30,42)(31,40)(32,44)(33,48)(36,68)(38,62)(39,63)(41,67)(43,64)(45,60)(47,65)(50,58)(53,81)(54,59)(55,79)(57,61)(66,76)(69,71)(70,78)(72,73)(74,77)(75,80);(18,21,22,38,24,40,44,41)(19,26,27,53,29,55,42,54)(20,31,32,62,35,37,34,67)(23,47,43,73,48,74,76,39)(25,49,30,59,51,79,52,81)(28,57,45,70,58,69,75,36)(33,65,64,63,46,77,66,72)(50,71,60,78,56,61,80,68)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6380);