Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60217 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C24×C4 |
| prime radical | C17×#3475 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
1914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27,31,28,30,32,38,34)(29,33,37,35,36,39,41,40);(19,22)(23,25)(27,32)(28,34)(33,39)(35,40);(26,28,31,32,30,34,38,27)(29,35,37,39,36,40,41,33);(18,20,21,24)(19,23,22,25)(26,29,30,36)(27,33,32,39)(28,35,34,40)(31,37,38,41);(29,36)(33,39)(35,40)(37,41)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53205);