Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33918 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3339 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
476 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)(18,19,22,21)(20,24,25,23)(26,27)(28,32)(29,33)(30,43)(31,34)(35,40)(36,41)(37,45)(38,48)(39,55)(42,49)(44,51)(46,54)(47,52)(50,56)(53,57);(18,20)(19,23)(21,24)(22,25)(26,28)(27,32)(29,38)(30,39)(31,37)(33,48)(34,45)(35,46)(36,47)(40,54)(41,52)(42,51)(43,55)(44,49)(50,57)(53,56);(18,21,22,19)(20,24,25,23)(27,33)(28,37)(29,40)(30,41)(32,44)(34,49)(35,36)(38,53)(42,56)(43,50)(45,48)(46,55)(47,57)(51,54);(20,25)(23,24)(27,34)(32,45)(33,49)(35,50)(36,43)(44,48)(46,57)(47,55)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26906);