Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C213 |
| direct product | C17×#62841 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
6624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(19,23)(24,29)(25,30)(31,33)(34,35,39,40)(36,43,38,41)(37,42,45,47)(44,49,46,48);(21,28)(25,30)(26,32)(31,33)(35,40)(37,45)(41,43)(44,46);(18,19)(20,24)(21,25)(22,23)(26,31)(27,29)(28,30)(32,33)(34,35)(36,41)(37,42)(38,43)(39,40)(44,48)(45,47)(46,49);(18,20,22,27)(19,24,23,29)(21,26,28,32)(25,31,30,33)(34,36,39,38)(35,41,40,43)(37,44,45,46)(42,48,47,49);(18,21,22,28)(19,25,23,30)(20,26,27,32)(24,31,29,33)(34,37)(35,42)(36,44)(38,46)(39,45)(40,47)(41,48)(43,49);(18,19)(20,24)(21,25)(22,23)(26,31)(27,29)(28,30)(32,33)(34,38,39,36)(35,43,40,41)(37,46,45,44)(42,49,47,48)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55829);