Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #2263 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#2263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C23×C11 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C8×C11 ◁ C2×C11×C16 ◁ G | |
112 conjugacy classes of subgroups.
| 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)(14,18)(15,27)(16,30)(17,19)(20,23)(21,24)(22,28)(25,37)(26,31)(29,43)(32,39)(33,38)(34,40)(35,41)(36,42);(13,18)(14,23)(15,24)(16,28)(19,31)(20,21)(22,37)(25,42)(26,40)(27,32)(29,41)(30,33)(34,35)(36,43)(38,39);(13,19)(18,31)(20,34)(21,35)(22,30)(27,43)(32,36)(33,37)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 995);