Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#21429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
1010 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)(20,23)(21,22)(24,25)(26,27,30,35,31,34,36,48)(28,32,39,44,38,45,42,49)(29,33,41,47,40,46,50,56)(37,43,52,55,51,54,53,57);(26,28,36,39,31,38,30,42)(27,32,35,49,34,45,48,44)(29,37,50,52,40,51,41,53)(33,43,47,57,46,54,56,55);(19,22)(23,25)(26,29,31,40)(27,33,34,46)(28,37,38,51)(30,41,36,50)(32,43,45,54)(35,47,48,56)(39,52,42,53)(44,55,49,57);(18,20,21,24)(19,23,22,25)(29,40)(33,46)(37,51)(41,50)(43,54)(47,56)(52,53)(55,57)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14417);