Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#60826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
2026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27,31,36)(28,32,37,45)(29,34,40,48)(30,33,42,35)(38,44,50,55)(39,46,51,43)(41,47,53,49)(52,56,57,54);(18,20,21,25)(19,22,23,24)(26,28)(27,32)(29,38)(30,39)(31,37)(33,46)(34,44)(35,43)(36,45)(40,50)(41,52)(42,51)(47,56)(48,55)(49,54)(53,57);(20,25)(22,24)(27,33)(28,37)(30,42)(32,43)(34,47)(35,36)(38,50)(41,53)(44,54)(45,46)(48,49)(55,56);(19,23)(22,24)(26,29)(27,34)(28,38)(30,41)(31,40)(32,44)(33,47)(35,49)(36,48)(37,50)(39,52)(42,53)(43,54)(45,55)(46,56)(51,57);(29,40)(34,48)(38,50)(41,53)(44,55)(47,49)(52,57)(54,56)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53814);