Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61350 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3035 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
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)(19,22)(23,24)(26,27,31,36)(28,38,40,33)(29,42,44,51)(30,37,32,35)(34,46,49,43)(39,53,54,57)(41,48,45,50)(47,56,52,55);(18,19,21,22)(20,24,25,23)(26,28,31,40)(27,33,36,38)(29,39,44,54)(30,45,32,41)(34,47,49,52)(35,50,37,48)(42,57,51,53)(43,56,46,55);(26,29)(27,34)(28,39)(30,43)(31,44)(32,46)(33,47)(35,42)(36,49)(37,51)(38,52)(40,54)(41,55)(45,56)(48,53)(50,57);(18,20,21,25)(19,23,22,24)(28,40)(33,38)(39,54)(41,45)(47,52)(48,50)(53,57)(55,56);(26,30,31,32)(27,35,36,37)(28,41,40,45)(29,43,44,46)(33,48,38,50)(34,42,49,51)(39,55,54,56)(47,53,52,57)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54338);