Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25183 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×H(5,𝔽2) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
1000 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,20)(22,23,28,34)(24,35,39,50)(25,41,26,31)(27,45,29,33)(30,40,47,38)(32,43,49,44)(36,48,52,51)(37,46,42,53);(18,20,21,19)(22,24,28,39)(23,30,34,47)(25,42,26,37)(27,40,29,38)(31,48,41,51)(32,46,49,53)(33,50,45,35)(36,44,52,43);(19,20)(22,25,28,26)(23,31,34,41)(24,36,39,52)(27,43,29,44)(30,46,47,53)(32,33,49,45)(35,51,50,48)(37,38,42,40);(22,26,28,25)(23,32,34,49)(24,37,39,42)(27,43,29,44)(30,46,47,53)(31,33,41,45)(35,48,50,51)(36,38,52,40)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18171);