Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C213 |
| direct product | C17×#62864 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
6666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 6 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,32)(22,26)(23,27)(24,31)(25,34)(29,44)(30,43)(33,47)(35,40)(36,42)(37,48)(38,46)(39,45)(41,49);(18,20,22,31)(19,24,26,28)(21,33,35,29)(23,30,36,46)(25,39,41,37)(27,38,42,43)(32,44,40,47)(34,48,49,45);(18,21,22,35)(19,25,26,41)(20,29,31,33)(23,34,36,49)(24,37,28,39)(27,32,42,40)(30,45,46,48)(38,47,43,44);(19,26)(21,34)(24,28)(25,40)(27,42)(29,45)(32,41)(33,48)(35,49)(37,44)(38,43)(39,47);(20,30)(24,38)(28,43)(29,45)(31,46)(33,48)(37,47)(39,44);(19,27)(24,38)(25,32)(26,42)(28,43)(37,47)(39,44)(40,41)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55852);