Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2190 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#2191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C11 |
| prime radical | C11×#575 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×M16 ◁ G | |
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,24,40)(15,26,28,42)(16,31,29,20)(18,33,34,23)(19,36,38,30)(25,41,32,37)(27,39,43,35);(12,14)(13,18)(15,27)(16,32)(17,24)(19,37)(20,39)(21,34)(22,26)(23,30)(25,29)(28,43)(31,35)(33,36)(38,41)(40,42);(15,28)(19,38)(22,40)(23,33)(26,42)(27,43)(30,36)(37,41)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 923);