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×#7450 |
| 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)(26,27,28,33,38,46,53,44,30,35,39,47,42,50,54,45,31,36,40,48,55,57,56,51,41,49,52,43,29,34,37,32);(18,19,21,23)(20,25,24,22)(27,32)(28,37)(29,38)(30,41)(33,34)(35,51)(36,45)(39,56)(40,54)(42,55)(43,46)(44,49)(47,57)(48,50)(52,53)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 438);