Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34594 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| prime radical | C17×#2656 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
2362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23)(24,28)(25,27)(26,29)(30,31)(32,34)(33,35)(36,37);(18,19,21,20)(22,24,26,25)(23,27,29,28)(30,32)(31,34)(33,36)(35,37);(18,20,21,19)(22,24,26,25)(23,28,29,27)(32,36)(34,37);(31,35)(34,37);(22,25,26,24)(23,27,29,28)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27582);