Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#9100 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | C2×C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,24,22,20,23,25)(26,27)(28,36)(29,40,42,33)(30,43)(31,35)(32,38)(34,45)(37,50,53,57)(39,51)(41,48,44,49)(46,52,56,54)(47,55);(18,20,21,25,22,19,23,24)(26,28,30,38,31,39,45,55)(27,32,34,36,35,47,43,51)(29,37,44,54,42,53,41,52)(33,46,49,50,40,56,48,57);(26,29,31,42)(27,33,35,40)(28,37,39,53)(30,44,45,41)(32,46,47,56)(34,49,43,48)(36,50,51,57)(38,54,55,52)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2088);