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) = C23 |
| direct product | C23×#421 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | C2×D4 |
| commutator | C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C4 | C23×C23 |
| socle | C2×C23 | C2×C22⋊C4 |
| prime radical | C2×#41×C23 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C22×C4×C23 ◁ G | |
154 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 368 |
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)(24,25,28,31,29,32,27,36)(26,33,35,30,34,39,37,38);(24,26)(25,30)(27,37)(28,35)(29,34)(31,39)(32,38)(33,36);(26,34)(30,38)(33,39)(35,37)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 102);