Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#7451 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | #357 |
| commutator | C2×C16 | C2×C4×C17 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ C4×C16×C17 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 2 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,24)(23,25)(26,27,29,35,45,54,57,33,32,38,28,39,31,37,46,51,30,36,43,50,41,52,40,49,48,55,42,34,47,53,44,56);(18,19,21,23)(20,25,24,22)(27,33)(28,40)(29,44)(31,41)(32,48)(34,37)(35,54)(36,49)(38,56)(39,53)(42,57)(43,46)(45,47)(50,52)(51,55)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 439);