Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#23874 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1674 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)(20,25)(21,32)(22,24)(23,28)(26,33)(27,35)(29,44)(30,39)(31,41)(34,43)(36,38)(37,42)(40,45)(46,48)(47,49);(19,24)(22,35)(25,39)(26,32)(27,28)(30,36)(33,37)(38,41)(40,44)(42,43)(45,47)(48,49);(18,20,23,31)(19,25,28,41)(21,29,34,46)(22,36,35,30)(24,38,27,39)(26,40,42,49)(32,48,43,44)(33,47,37,45);(18,21)(19,26)(20,29)(22,37)(23,34)(24,32)(25,40)(27,43)(28,42)(30,47)(31,46)(33,35)(36,45)(38,48)(39,44)(41,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16862);