Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13391 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2033 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
390 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)(18,19)(20,31)(21,35)(22,37)(23,39)(24,28)(25,30)(26,32)(27,36)(29,38)(33,43)(34,44)(40,42)(41,45)(46,49)(47,48);(18,20)(19,26)(21,22)(23,33)(24,32)(25,34)(27,45)(28,44)(29,43)(30,35)(31,37)(36,38)(39,47)(40,48)(41,49)(42,46);(18,21,22,20,25,32,24,34)(19,27,28,46,30,47,37,43)(23,33,38,48,41,49,40,36)(26,42,31,45,35,29,44,39)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6379);