Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#560 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ G | |
252 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)(26,33)(27,32)(28,30)(29,35)(31,37)(34,38)(36,39);(24,26)(25,29)(27,35)(28,36)(30,38)(31,39)(32,33)(34,37);(25,30)(26,34)(29,33)(31,32)(35,36)(38,39);(25,31)(26,35)(29,38)(30,32)(33,39)(34,36)437 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 241);