Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8790 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C8 |
| direct product | C17×#8793 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #382 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #124 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
294 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)(19,20)(21,22)(24,25)(26,27)(28,36,40,32)(29,41,43,56)(30,35)(31,34)(33,42,47,51)(37,44)(38,52)(39,49,50,46)(45,53)(48,57)(54,55);(18,19,21,20,23,25,22,24)(26,28,37,50,31,40,30,39)(27,32,44,49,34,36,35,46)(29,38,51,57,43,54,42,53)(33,45,56,52,47,48,41,55);(18,20,22,19,23,24,21,25)(26,29,31,43)(27,33)(28,38,40,54)(30,42,37,51)(32,45)(34,47)(35,41)(36,48)(39,53,50,57)(44,56)(46,55)(49,52)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1781);