Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#418 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×D4 |
| commutator | C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C4 | C23×C23 |
| prime radical | C22×D4×C23 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 368 |
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)(30,34)(31,33)(32,35);(29,33)(30,31)(34,35);(28,30,32,31)(29,34,35,33)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 99);