Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18162 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18188 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
934 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)(20,27)(21,25)(22,31)(23,26)(24,29)(28,32)(30,33)(39,45)(46,49);(18,20,23,30)(19,24,26,32)(21,29,22,28)(25,33,31,27)(34,35)(36,39)(37,40)(38,41)(42,46)(43,45)(44,47)(48,49);(34,36,38,43)(35,39,41,45)(37,42,44,48)(40,46,47,49);(18,21,23,22)(19,25,26,31)(20,28,30,29)(24,27,32,33)(34,37,38,44)(35,40,41,47)(36,42,43,48)(39,46,45,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11176);