Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C213 |
| direct product | C2×C17×#3538 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| prime radical | C2×C17×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
7162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 6 generators on 43 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(4,7)(5,9)(11,12,16,18)(13,19,21,14)(15,23,24,17)(20,22,26,25);(4,7)(8,10)(11,13,16,21)(12,14,18,19)(15,20,24,26)(17,22,23,25);(3,4)(5,8)(6,7)(9,10);(3,5)(4,8)(6,9)(7,10)(11,14)(12,13)(15,22)(16,19)(17,20)(18,21)(23,26)(24,25);(11,15,16,24)(12,17,18,23)(13,20,21,26)(14,22,19,25)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55713);