Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#543 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C23 |
| prime radical | C24×C23 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ G | |
242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,31)(26,32,34,30)(27,29,35,37)(33,38,39,36);(25,29)(26,33)(31,37)(34,39);(24,26,28,34)(25,30,31,32)(27,33,35,39)(29,36,37,38);(25,29)(30,36)(31,37)(32,38)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 224);