Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C2×C4 |
| direct product | C23×#486 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C23 |
| prime radical | C23×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 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)(26,29)(27,28)(30,31)(33,38)(34,39)(35,36);(25,28)(29,31)(32,33,36,34,37,39,35,38);(24,26,27,30)(25,29,28,31)(32,34,35,33,37,38,36,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 167);