Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#20913 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×#41×C17 ◁ G | |
1778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23)(24,25)(26,27,30,32,31,35,29,34)(28,33,38,39,36,40,37,41);(18,19,20,21)(27,32)(29,30)(33,39)(34,35)(37,38)(40,41);(23,25)(26,28)(27,33)(29,37)(30,38)(31,36)(32,39)(34,41)(35,40);(28,36)(33,40)(37,38)(39,41)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13901);