Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C11×H(5,𝔽2) ⋊ C2 |
| Sylow | C11 ⋊ #3488 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C2×C11×H(5,𝔽2) | C2 |
| hypercenter | C2×H(5,𝔽2) | D11 |
| hypocenter | C11 | #3488 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
1658 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^10214 conjugacy classes — view the full character table.
| maximal subgroup of | #14785107, #14785118, #14785129, … |
| maximal normal subgroup of | #14785107, #14785118, #14785129, … |
| maximal quotient of | #14913806, #14914076, #14914106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18172);