Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10187 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,21)(24,25)(26,27,32,37)(28,33,40,49)(29,41,43,52)(30,36,31,35)(34,45,51,44)(38,50,54,57)(39,53,46,48)(42,47,55,56);(18,19,22,24)(20,23,21,25)(26,28)(27,33)(29,42)(30,39)(31,46)(32,40)(34,50)(35,48)(36,53)(37,49)(38,45)(41,56)(43,55)(44,54)(47,52)(51,57);(18,20,22,21)(19,23,24,25)(26,29)(27,34)(28,38)(30,45)(31,44)(32,43)(33,47)(35,52)(36,41)(37,51)(39,55)(40,54)(42,46)(48,57)(49,56)(50,53)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3175);