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×#436 |
| 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 | C2×D4×C23 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 35 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)(26,27)(28,29,32,30,31,33,35,34);(25,27)(29,33)(30,34);(28,30,32,33,31,34,35,29)644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 117);