Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#432 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C23 |
| commutator | C22 | C22×C4×C23 |
| Frattini, cosocle | C2×C4 | C23×C23 |
| socle | C22×C23 | C22×C4 |
| prime radical | C23×C23 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ G | |
110 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)(32,33,34,37,35,36,38,39);(25,28)(29,31);(24,26,27,30)(25,29,28,31)(33,36)(37,39)644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 113);