Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#23649 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#397 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
892 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,31,41)(21,25)(22,26)(23,27)(24,30,38,35)(29,44,32,43)(33,39)(34,40)(36,42)(37,46,48,45)(47,49);(18,20)(19,24)(21,32)(22,35)(23,31)(25,37)(26,41)(27,38)(28,42)(29,33)(30,36)(34,45)(39,48)(40,44)(43,49)(46,47);(18,21,22,34,23,33,36,47)(19,25,26,40,27,39,42,49)(20,29,30,45,31,32,35,46)(24,37,28,43,38,48,41,44);(21,33)(25,39)(29,32)(34,47)(37,48)(40,49)(43,44)(45,46)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16637);