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×#34059 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| prime radical | C24×C17 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
2250 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)(22,23)(24,27)(25,26)(28,29)(30,31)(32,38)(33,36)(34,37)(35,40)(39,44)(41,43)(42,45);(30,32,34,40)(31,35,37,38)(33,41,42,39)(36,44,45,43);(23,26)(27,29)(30,33,34,42)(31,36,37,45)(32,39,40,41)(35,43,38,44);(31,37)(35,38)(36,45)(43,44);(22,24,25,28)(23,27,26,29)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27047);