Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(23,26)(24,28)(30,31)(32,39)(33,36)(34,42)(35,38)(37,43)(40,44)(41,45);(23,26)(27,29)(30,32,35,33)(31,36,38,39)(34,40,43,41)(37,44,42,45);(18,20,21,19)(22,23)(24,27)(25,26)(28,29)(30,33,35,32)(31,36,38,39)(34,41,43,40)(37,44,42,45);(22,24)(23,27)(25,28)(26,29)(30,31)(32,39)(33,36)(34,37)(35,38)(40,45)(41,44)(42,43);(30,34,35,43)(31,37,38,42)(32,40,33,41)(36,44,39,45)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27400);