Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9928 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C25×C17 | D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 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)(22,23,25,28)(24,26,29,27)(30,31,34,37)(32,38,40,45)(33,41,43,36)(35,42,44,39);(23,26)(24,29)(27,28)(30,32,34,40)(31,35,37,44)(33,42,43,39)(36,45,41,38);(19,21)(24,29)(26,27)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2916);