Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#11029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #121 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
1242 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)(20,21)(26,27,31,37,32,35,30,36)(28,38,41,49,42,33,40,50)(29,43,46,52,47,34,45,53)(39,48,55,57,56,54,44,51);(19,21)(22,23)(24,25)(26,28,32,42)(27,33,35,38)(29,44,47,55)(30,41,31,40)(34,51,43,57)(36,50,37,49)(39,46,56,45)(48,53,54,52);(23,25)(26,29,32,47)(27,34,35,43)(28,39,42,56)(30,46,31,45)(33,48,38,54)(36,53,37,52)(40,55,41,44)(49,57,50,51)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4017);