Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C11×SD16 ⋊ C2 |
| Sylow | C11 ⋊ #2949 |
492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,d^c=dg,h^d=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2949, C2×#13077470, #15617940, … |
| maximal normal subgroup of | D11×#2949, C2×#13077470, #15617940, … |
| maximal quotient of | #14723233, #14723448, #14723457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13364);