Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18562 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18593 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3511 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
916 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)(20,27)(21,25)(22,31)(23,26)(24,28)(29,33)(30,32)(34,35,39,43)(36,44,47,48)(37,40,38,42)(41,46,49,45);(18,20,23,30)(19,24,26,33)(21,28,22,29)(25,32,31,27)(35,40)(37,38)(41,48)(42,43)(44,49)(45,46);(18,21,23,22)(19,25,26,31)(20,28,30,29)(24,32,33,27)(34,36,39,47)(35,41,43,49)(37,45,38,46)(40,48,42,44);(18,21,23,22)(19,25,26,31)(20,29,30,28)(24,27,33,32)(34,37,39,38)(35,40,43,42)(36,45,47,46)(41,48,49,44)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11581);