Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#22205 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C17×#3054 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27,31,35,32,36,30,45)(28,33,39,47,40,48,38,54)(29,41,44,49,42,55,43,34)(37,50,53,56,51,57,52,46);(18,20)(19,22)(21,25)(23,24)(26,28,31,39,32,40,30,38)(27,33,35,47,36,48,45,54)(29,37,44,53,42,51,43,52)(34,46,41,50,49,56,55,57);(20,25)(22,24)(26,29,30,43,32,42,31,44)(27,34,35,41,36,49,45,55)(28,37,38,52,40,51,39,53)(33,46,47,50,48,56,54,57);(19,23)(22,24)(29,42)(34,49)(37,51)(41,55)(43,44)(46,56)(50,57)(52,53)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15193);