Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C11×#557 ⋊ C2 |
| Sylow | C11 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C11×#557 | C2 |
| prime radical | C2×#4343 | C22 |
| hypercenter | #557 | D11 |
| hypocenter | C11 | Q8×#41 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #557 | |
1068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^b=h^10,h^d=h^10,h^e=h^10175 conjugacy classes — view the full character table.
| maximal subgroup of | #14729752, #14729760, #14729767, … |
| maximal normal subgroup of | #14729752, #14729760, #14729767, … |
| maximal quotient of | C4⋊C4×#4343, #14913090, #14913200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18092);