Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C23 · Schur multiplier (H2) = C2×C42 |
| direct product | C23×#376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C23 | C22 |
| commutator | C2 | C2×C42×C23 |
| Frattini, cosocle | C23 | C23×C23 |
| socle, prime radical | C23×C23 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C23 ◁ G | |
178 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)(24,25,26,27)(32,33)(34,37)(35,36)(38,39);(28,29,30,31)(33,36)(37,39);(32,34,35,38)(33,37,36,39)920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 57);