Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C11 ⋊ #3502 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C2×C4×Q8×C11 | C2 |
| prime radical | C23×C11 | C24 |
| hypercenter | C2×C4×Q8 | D11 |
| hypocenter | C11 | #3502 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 | |
964 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 964 conjugacy classes of subgroups — too many to draw. Only its 553 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=f,c^2=g,d^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^10,d^b=df244 conjugacy classes — view the full character table.
| maximal subgroup of | #14645335, #14645338, #14645772, … |
| maximal normal subgroup of | #14645335, #14645338, #14645772, … |
| maximal quotient of | #14913870, #14914213, #14914711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18320);