Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C23×C4 |
| direct product | C23×#555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ G | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 736 |
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)(26,30)(27,31)(28,29)(33,34)(37,38);(25,29)(27,30)(32,33,36,34)(35,38,39,37);(24,26,28,31)(25,30,29,27)(32,34,36,33)(35,38,39,37);(24,27,28,30)(25,31,29,26)(32,35,36,39)(33,37,34,38)575 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 236);