Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13402 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2034 |
| 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 | |
384 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)(21,36,41,71)(22,42,44,27)(23,45,47,69)(25,34,51,32)(26,52,56,39)(28,57,59,43)(31,61,64,81)(33,49,68,79)(37,72,62,80)(38,70,40,58)(46,55,73,54)(48,76,78,66)(53,75,77,63)(60,65,74,67);(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)(36,61)(38,64)(39,66)(41,62)(43,67)(45,74)(46,75)(47,68)(48,55)(52,76)(54,78)(56,77)(57,65)(58,80)(59,79)(60,69)(63,73)(70,72)(71,81);(18,21,24,41)(19,26,29,56)(20,31)(22,40,44,38)(23,46,47,73)(25,48)(27,55,42,54)(28,58,59,70)(30,53)(32,37)(33,66)(34,62)(35,64)(36,69,71,45)(39,57,52,43)(49,61)(50,77)(51,78)(60,80)(63,67)(65,75)(68,76)(72,74)(79,81)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6391);