Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10078 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#10426 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C22×D4×C17 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
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)(19,20)(24,29)(26,28)(30,31)(32,36)(33,37)(34,38)(35,39)(40,43)(41,44)(42,45);(18,19)(20,21)(22,23)(24,26)(25,27)(28,29)(30,32,35,42)(31,36,39,45)(33,41,34,40)(37,44,38,43);(18,20,21,19)(23,26)(24,29)(27,28)(31,37)(32,40)(33,34)(38,39)(41,42)(43,44)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3414);