Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18125 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
928 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(18,19,22,25)(20,26,28,33)(21,29,31,24)(23,30,32,27)(39,45)(46,49);(18,20,22,28)(19,23,25,32)(21,30,31,27)(24,33,29,26)(34,35)(36,39)(37,40)(38,41)(42,46)(43,45)(44,47)(48,49);(34,36)(35,39)(37,42)(38,43)(40,46)(41,45)(44,48)(47,49);(34,37,38,44)(35,40,41,47)(36,42,43,48)(39,46,45,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11113);