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×#32895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
3540 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)(19,25)(20,29)(22,23)(27,42)(28,34)(30,44)(31,36)(32,35)(37,40)(38,43)(39,48)(45,46);(18,19)(20,26)(21,27)(22,34)(23,25)(24,28)(29,40)(30,39)(31,41)(32,38)(33,43)(35,42)(36,37)(44,49)(45,47)(46,48);(18,20,24,31)(19,26,28,41)(21,30,33,46)(22,29,23,36)(25,37,34,40)(27,39,43,48)(32,45,35,44)(38,47,42,49);(18,21)(19,27)(20,30)(22,35)(23,32)(24,33)(25,38)(26,39)(28,43)(29,44)(31,46)(34,42)(36,45)(37,47)(40,49)(41,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 25883);