Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C17×#491 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C2×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle, prime radical | C23×C17 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C43×C17 ◁ G | |
802 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(5,6)(7,10)(8,9)(11,12)(13,14,19,24)(15,21,26,27)(16,20,25,28)(17,23,18,22);(6,9)(10,12)(13,15,17,16,19,26,18,25)(14,20,22,21,24,28,23,27);(5,7,8,11)(6,10,9,12)(13,16,17,26,19,25,18,15)(14,21,22,28,24,27,23,20)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14639);