Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34634 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
2374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1088 |
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)(22,23,25,27)(24,28,29,26)(30,31)(32,35)(33,37)(34,36)(38,41)(39,42)(40,43)(44,45);(22,24,25,29)(23,26,27,28)(30,32)(31,35)(33,39)(34,38)(36,41)(37,42)(40,44)(43,45);(19,21)(32,38)(35,41)(39,44)(42,45);(31,36)(35,41)(37,43)(42,45);(30,33,34,40)(31,37,36,43)(32,39,38,44)(35,42,41,45)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27622);