Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(23,29)(24,28)(25,33)(26,38)(30,46)(31,48)(32,45)(34,41)(35,50)(36,49)(37,43)(39,42)(44,51)(47,52);(22,23,27,32)(24,30,28,42)(25,35,37,48)(26,39,41,46)(29,34,45,38)(31,49,50,36)(33,52,43,44)(40,47,53,51);(19,21)(22,24,27,28)(23,30,32,42)(25,33,37,43)(26,34,41,38)(29,39,45,46)(31,47,50,51)(35,52,48,44)(36,40,49,53);(22,25,27,37)(23,31,32,50)(24,33,28,43)(26,40,41,53)(29,44,45,52)(30,47,42,51)(34,49,38,36)(35,46,48,39)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26825);