Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
318 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)(18,19,22,24)(20,25,21,23)(26,27)(28,32)(29,33)(30,35)(31,37)(34,42)(36,43)(38,51)(39,48)(40,46)(41,47)(44,50)(45,52)(49,55)(53,57)(54,56);(18,20,22,21)(19,23,24,25)(26,28)(27,32)(29,39)(30,38)(31,41)(33,48)(34,45)(35,51)(36,46)(37,47)(40,43)(42,52)(44,53)(49,56)(50,57)(54,55);(18,21,22,20)(19,23,24,25)(27,33)(28,38)(29,42)(30,43)(32,45)(34,36)(35,49)(37,50)(39,53)(40,41)(44,55)(46,57)(47,56)(48,51)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6443);