Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13389 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13390 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2033 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
382 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)(18,19,24,29)(20,30,35,50)(21,36,40,71)(22,42,44,27)(23,45,47,76)(25,34,51,32)(26,52,55,39)(28,57,59,43)(31,62,37,73)(33,49,68,80)(38,72,41,58)(46,56,75,54)(48,66,53,78)(60,74,81,64)(61,65,77,67)(63,79,69,70);(18,20)(19,25)(21,37)(22,34)(23,33)(24,35)(26,53)(27,50)(28,49)(29,51)(30,42)(31,40)(32,44)(36,70)(38,63)(39,74)(41,69)(43,67)(45,77)(46,78)(47,68)(48,55)(52,64)(54,60)(56,81)(57,65)(58,62)(59,80)(61,76)(66,75)(71,79)(72,73);(18,21,22,38,24,40,44,41)(19,26,27,54,29,55,42,56)(20,31,32,63,35,37,34,69)(23,46,43,52,47,75,57,39)(25,48,30,60,51,53,50,81)(28,58,45,71,59,72,76,36)(33,66,65,64,68,78,67,74)(49,73,61,79,80,62,77,70)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6378);