Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×C17×#1899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C24×C4×C17 ◁ G | |
2066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4)(5,6)(7,8)(9,12,16,19)(10,13)(11,14)(15,18,21,22)(17,20);(7,9)(8,12,14,19)(10,15)(11,16)(13,18,20,22)(17,21);(4,6)(7,10,11,17)(8,13,14,20)(9,15,16,21)(12,18,19,22)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13970);