Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61634 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3486 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#525 ◁ G | |
2018 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)(26,27,31,35)(28,32,37,46)(29,39,41,49)(30,42,44,34)(33,43,48,40)(36,50,51,57)(38,54,53,47)(45,55,56,52);(18,20)(19,22)(21,25)(23,24)(26,28,31,37)(27,32,35,46)(29,36,41,51)(30,38,44,53)(33,45,48,56)(34,47,42,54)(39,50,49,57)(40,52,43,55);(26,29,31,41)(27,33,35,48)(28,36,37,51)(30,43,44,40)(32,45,46,56)(34,49,42,39)(38,55,53,52)(47,57,54,50);(20,25)(22,24)(28,37)(32,46)(36,51)(38,53)(45,56)(47,54)(50,57)(52,55);(19,23)(22,24)(28,37)(32,46)(36,51)(38,53)(45,56)(47,54)(50,57)(52,55)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54622);