Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D11 |
| commutator, socle | C2×C11 | C22×C16 |
| Fitting | C11×#504 | C2 |
| prime radical | C11×#41 | C8 |
| cosocle | C11×C16 | C23 |
| hypercenter | #504 | D11 |
| hypocenter | C11 | #2258 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C16 ◁ #504 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^10,c^b=cg280 conjugacy classes — view the full character table.
| maximal subgroup of | #14674334, #14674337, #14674339, … |
| maximal normal subgroup of | #14674334, #14674337, #14674339, … |
| maximal quotient of | #14673953, #14673970, #14674259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6804);