Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61054 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#525 ◁ G | |
2710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 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)(22,23)(24,33)(25,30)(26,31)(27,40)(28,32)(29,34)(35,50)(36,43)(37,46)(38,53)(39,48)(41,45)(42,49)(44,51)(47,52);(22,24,28,36)(23,29,32,45)(25,34,27,41)(26,38,39,51)(30,43,40,33)(31,47,48,50)(35,42,52,37)(44,46,53,49);(19,21)(22,25,28,27)(23,30,32,40)(24,34,36,41)(26,37,39,42)(29,43,45,33)(31,46,48,49)(35,51,52,38)(44,47,53,50);(22,26,28,39)(23,31,32,48)(24,35,36,52)(25,37,27,42)(29,44,45,53)(30,46,40,49)(33,50,43,47)(34,51,41,38);(23,32)(29,45)(30,40)(31,48)(33,43)(44,53)(46,49)(47,50)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54042);