Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #3489 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C2×C11×C22⋊Q8 | C2 |
| hypercenter | C2×C22⋊Q8 | D11 |
| hypocenter | C11 | #3489 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊Q8 | |
1522 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14645974, #14645978, #14721404, … |
| maximal normal subgroup of | #14645974, #14645978, #14721404, … |
| maximal quotient of | #14913809, #14914074, #14914080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18186);