Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C213 |
| direct product | C17×#62851 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
7066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 6 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,25)(26,27)(28,31)(29,30)(32,40)(33,35)(34,41)(36,37)(38,39);(18,19,21,22)(20,23,24,25)(26,28,33,30)(27,29,35,31)(32,36,41,38)(34,37,40,39);(26,29,33,31)(27,28,35,30)(32,37,41,39)(34,36,40,38);(26,30,33,28)(27,29,35,31)(32,38,41,36)(34,37,40,39);(18,20,21,24)(19,23,22,25)(26,31,33,29)(27,28,35,30)(32,39,41,37)(34,36,40,38);(26,32)(27,34)(28,36)(29,37)(30,38)(31,39)(33,41)(35,40)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55839);