Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C11×C64 ⋊ C2 |
| Sylow | C11 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×D11 |
| commutator, socle | C2×C11 | C2×C32 |
| Fitting | C11×C64 | C2 |
| prime radical | C2×D11 | C32 |
| cosocle | C11×C32 | C22 |
| hypercenter | C64 | D11 |
| hypocenter | C11 | M128 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C32 ◁ C64 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^10400 conjugacy classes — view the full character table.
| maximal subgroup of | D11×M128, C2×#13066826, #14674811, … |
| maximal normal subgroup of | D11×M128, C2×#13066826, #14674811, … |
| maximal quotient of | #14641577, (C2×D11)⋊C64, Dic11⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2720);