Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#34197 |
| 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 | |
2314 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)(18,19,20,21)(23,26)(27,29)(31,32)(34,42)(36,38)(40,45);(30,31,35,32)(33,38,41,36)(34,37,42,39)(40,44,45,43);(22,23)(24,27)(25,26)(28,29)(30,32,35,31)(33,38,41,36)(34,39,42,37)(40,44,45,43);(30,33,35,41)(31,36,32,38)(34,40,42,45)(37,43,39,44);(22,24,25,28)(23,27,26,29)(30,34)(31,37)(32,39)(33,40)(35,42)(36,43)(38,44)(41,45)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27185);