Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18521 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| prime radical | C17×#3480 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(18,19,23,26)(20,27,29,32)(21,25,22,30)(24,31,33,28)(34,35,40,45)(36,46,48,42)(37,49,47,41)(38,43,39,44);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,33)(27,30)(34,36)(35,41)(37,38)(39,47)(40,48)(42,44)(43,46)(45,49);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(34,37,40,47)(35,42,45,46)(36,38,48,39)(41,44,49,43);(34,38,40,39)(35,43,45,44)(36,37,48,47)(41,46,49,42)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11509);