Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#2634 |
| 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 | |
416 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 192 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)(17,20)(21,23)(24,25,29,27)(26,32,34,30)(28,31,36,35)(33,38,39,37);(13,15)(17,20)(21,23)(24,26,29,34)(25,30,27,32)(28,33,36,39)(31,37,35,38);(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,27,29,25)(26,30,34,32)(28,31,36,35)(33,38,39,37);(16,18,19,22)(17,21,20,23)(24,28)(25,31)(26,33)(27,35)(29,36)(30,37)(32,38)(34,39)352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1366);