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) = C2 |
| direct product | C23×#446 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C23 |
| commutator | C22 | C22×C4×C23 |
| Frattini, cosocle | C2×C4 | C23×C23 |
| socle, prime radical | C22×C23 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ G | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1472 |
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)(26,31)(27,29)(28,30)(32,33,35,34,36,37,39,38);(24,26,28,27)(25,29,30,31);(24,27,28,26)(25,29,30,31)(32,34,35,37,36,38,39,33)644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 127);