Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C11×#123 ⋊ C2 |
| Sylow | C11 ⋊ #3535 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C2×C11×#123 | C2 |
| hypercenter | C2×#123 | D11 |
| hypocenter | C11 | #3535 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C2×#123 | |
1038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|b^2=f,d^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^10,c^b=cg,d^b=df,h^b=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | #14646105, #14646109, #14726953, … |
| maximal normal subgroup of | #14646105, #14646109, #14726953, … |
| maximal quotient of | #14916537, #14916703, #14916841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18723);