Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C23×C42 |
| direct product | C17×#21802 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
1194 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)(26,27,30,35,31,34,43,48)(28,32,38,46,37,45,53,56)(29,39,40,49,41,33,42,47)(36,50,52,57,51,44,54,55);(18,20,21,25)(19,22,23,24)(26,28)(27,32)(29,36)(30,38)(31,37)(33,44)(34,45)(35,46)(39,50)(40,52)(41,51)(42,54)(43,53)(47,55)(48,56)(49,57);(20,25)(22,24)(26,29,31,41)(27,33,34,39)(28,36,37,51)(30,42,43,40)(32,44,45,50)(35,49,48,47)(38,54,53,52)(46,57,56,55);(19,23)(22,24)(28,37)(32,45)(36,51)(38,53)(44,50)(46,56)(52,54)(55,57)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14790);