Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61207 |
| 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 ◁ C17×#532 ◁ G | |
2046 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)(18,19,21,23)(20,24,25,22)(26,27)(28,33)(29,35)(30,36)(31,45)(32,37)(34,41)(38,47)(39,48)(40,50)(42,51)(43,49)(44,52)(46,54)(53,56)(55,57);(18,20)(19,22)(21,25)(23,24)(26,28,32,40)(27,33,37,50)(29,38,42,55)(30,43,31,39)(34,46,52,56)(35,47,51,57)(36,49,45,48)(41,54,44,53);(26,29)(27,34)(28,38)(30,41)(31,44)(32,42)(33,46)(35,45)(36,51)(37,52)(39,53)(40,55)(43,54)(47,48)(49,57)(50,56);(20,25)(22,24)(26,29)(27,35)(28,38)(30,44)(31,41)(32,42)(33,47)(34,45)(36,52)(37,51)(39,54)(40,55)(43,53)(46,48)(49,56)(50,57);(26,30,32,31)(27,36,37,45)(28,39,40,43)(29,41,42,44)(33,48,50,49)(34,51,52,35)(38,53,55,54)(46,47,56,57)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54195);