Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61484 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#121 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1750 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)(23,25)(26,27,30,34)(28,36,38,32)(29,40,41,49)(31,44,43,35)(33,45,48,42)(37,52,53,57)(39,47,55,51)(46,54,50,56);(18,19)(20,23)(21,22)(24,25)(26,28)(27,32)(29,37)(30,38)(31,39)(33,46)(34,36)(35,47)(40,57)(41,53)(42,54)(43,55)(44,51)(45,56)(48,50)(49,52);(26,29,30,41)(27,33,34,48)(28,37,38,53)(31,45,43,42)(32,46,36,50)(35,49,44,40)(39,56,55,54)(47,52,51,57);(19,22)(23,25)(28,38)(32,36)(37,53)(39,55)(46,50)(47,51)(52,57)(54,56);(18,20,21,24)(19,23,22,25)(28,38)(32,36)(37,53)(39,55)(46,50)(47,51)(52,57)(54,56)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54472);