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×#62843 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
7130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(18,19,21,23)(20,24,25,22)(26,27)(28,32)(29,36)(30,31)(33,37)(34,38)(35,41)(39,40);(18,20,21,25)(19,22,23,24)(28,34)(32,38)(35,40)(39,41);(27,31)(32,38)(33,36)(39,41);(26,27)(28,32)(29,33)(30,31)(34,38)(35,39)(36,37)(40,41);(26,28)(27,32)(29,35)(30,34)(31,38)(33,39)(36,41)(37,40);(26,29)(27,33)(28,35)(30,37)(31,36)(32,39)(34,40)(38,41)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55831);