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×#13389 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2033 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,25)(20,29)(21,23)(22,35)(26,41)(27,44)(28,33)(30,48)(31,36)(32,47)(34,37)(38,46)(39,42)(43,45);(18,19)(20,30)(21,33)(22,27)(23,25)(24,28)(26,32)(29,45)(31,39)(34,49)(35,40)(36,48)(37,44)(38,43)(41,46)(42,47);(18,20,21,31,24,32,23,38)(19,26,25,39,28,30,33,43)(22,36,34,29,37,46,35,47)(27,41,40,45,44,48,49,42)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6377);