Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18269 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
924 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)(20,23,27,30)(21,24,28,31)(26,32,33,29)(35,40)(37,38)(41,48)(42,46)(43,44)(47,49);(18,20)(19,23)(21,26)(22,27)(24,29)(25,30)(28,33)(31,32)(34,35)(36,41)(37,40)(38,46)(39,42)(43,48)(44,47)(45,49);(18,21)(19,24)(20,26)(22,28)(23,29)(25,31)(27,33)(30,32)(34,36,39,45)(35,41,42,49)(37,44,38,43)(40,47,46,48);(34,37,39,38)(35,40,42,46)(36,43,45,44)(41,48,49,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11257);