Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#2822 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
380 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(17,18)(21,22)(24,25,29,31)(26,32,34,27)(28,30,38,39)(33,37,36,35);(13,15)(16,17,20,18)(19,21,23,22)(24,26,29,34)(25,27,31,32)(28,36,38,33)(30,37,39,35);(12,13)(14,15)(16,18,20,17)(19,21,23,22)(24,27)(25,26)(28,37)(29,32)(30,36)(31,34)(33,39)(35,38);(16,19,20,23)(17,21,18,22)(24,28,29,38)(25,30,31,39)(26,33,34,36)(27,35,32,37)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1554);