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×#33678 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#2184 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#117 ◁ C17×#405 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(28,32)(29,33)(30,43)(31,36)(34,40)(35,41)(37,45)(38,44)(39,53)(42,49)(46,52)(47,51)(48,54)(50,55)(56,57);(19,22)(23,25)(26,28)(27,32)(29,38)(30,39)(31,37)(33,44)(34,46)(35,47)(36,45)(40,52)(41,51)(42,50)(43,53)(48,56)(49,55)(54,57);(27,33)(29,40)(30,41)(32,44)(34,35)(36,49)(38,52)(39,51)(42,54)(43,48)(45,55)(46,47)(50,57)(53,56);(18,20,21,24)(19,23,22,25)(28,37)(32,45)(38,50)(39,51)(44,55)(46,56)(47,53)(52,57)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26666);