Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13442 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13443 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2054 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
378 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)(18,19,25,31)(20,32,37,67)(21,38,44,74)(22,29,47,64)(23,28,48,63)(24,49,46,30)(26,51,55,34)(27,56,61,41)(33,68,72,52)(35,54,45,65)(36,53,50,62)(39,75,69,80)(40,60,42,78)(43,58,77,59)(57,70,66,79)(71,73,76,81);(18,20)(19,26)(21,39)(22,45)(23,34)(24,50)(25,37)(27,57)(28,62)(29,32)(30,65)(31,55)(33,42)(35,47)(36,46)(38,73)(40,72)(41,71)(43,79)(44,69)(48,51)(49,54)(52,59)(53,63)(56,76)(58,68)(60,75)(61,66)(64,67)(70,77)(74,81)(78,80);(18,21,22,40,46,77,48,56,25,44,47,42,24,43,23,41)(19,27,28,58,49,78,64,74,31,61,63,59,30,60,29,38)(20,33,34,69,50,76,35,70,37,72,51,39,36,71,45,79)(26,52,32,66,65,81,53,80,55,68,67,57,54,73,62,75)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6431);