Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#32896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×H(7,𝔽2) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
3610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,24,30)(20,31,34,44)(21,27,36,43)(22,29,23,28)(25,37,41,33)(26,38,42,35)(32,39,49,46)(40,48,45,47);(18,20)(19,25)(21,32)(22,37)(23,33)(24,34)(26,39)(27,40)(28,44)(29,31)(30,41)(35,48)(36,49)(38,47)(42,46)(43,45);(18,21)(19,26)(20,32)(22,35)(23,38)(24,36)(25,39)(27,28)(29,43)(30,42)(31,45)(33,47)(34,49)(37,48)(40,44)(41,46);(18,21)(19,27)(20,32)(22,38)(23,35)(24,36)(25,40)(26,28)(29,42)(30,43)(31,46)(33,48)(34,49)(37,47)(39,44)(41,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 25884);