Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ C2×C17×#131 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27,32,37)(28,33,40,51)(29,35,31,47)(30,43,46,57)(34,52,54,39)(36,42,55,45)(38,48,41,50)(44,49,56,53);(19,22)(23,25)(26,28)(27,33)(29,41)(30,39)(31,38)(32,40)(34,43)(35,50)(36,49)(37,51)(42,56)(44,45)(46,52)(47,48)(53,55)(54,57);(18,20,21,24)(19,23,22,25)(26,28)(27,34)(29,38)(30,44)(31,41)(32,40)(33,43)(35,49)(36,50)(37,54)(39,45)(42,52)(46,56)(47,53)(48,55)(51,57);(26,29,32,31)(27,35,37,47)(28,38,40,41)(30,42,46,45)(33,48,51,50)(34,49,54,53)(36,43,55,57)(39,44,52,56)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26641);