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×#33651 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ C2×C17×#131 ◁ G | |
556 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)(26,27,31,36)(28,32,37,45)(29,33,42,49)(30,43,41,35)(34,50,48,40)(38,44,51,55)(39,54,52,47)(46,57,56,53);(19,22)(23,25)(26,28)(27,32)(29,38)(30,39)(31,37)(33,44)(34,46)(35,47)(36,45)(40,53)(41,52)(42,51)(43,54)(48,56)(49,55)(50,57);(18,20,21,24)(19,23,22,25)(27,33)(29,40)(30,41)(32,44)(34,35)(36,49)(38,53)(39,52)(42,50)(43,48)(45,55)(46,47)(51,57)(54,56);(28,37)(32,45)(38,51)(39,52)(44,55)(46,56)(47,54)(53,57)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26639);