Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×C17×#2310 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
5214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(4,6)(7,8,9,10)(12,16)(13,19)(14,22)(24,26);(11,12,15,16)(13,20,19,17)(14,18,22,23)(21,26,25,24);(3,4)(5,6)(7,8)(9,10)(11,13,15,19)(12,17,16,20)(14,21,22,25)(18,24,23,26);(11,14)(12,18)(13,21)(15,22)(16,23)(17,24)(19,25)(20,26)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27030);