Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C11×#556 ⋊ C2 |
| Sylow | C11 ⋊ #3520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C11×#556 | C2 |
| hypercenter | #556 | D11 |
| hypocenter | C11 | #3520 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #556 | |
1124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^10,h^c=h^10,h^d=h^10,h^e=h^10169 conjugacy classes — view the full character table.
| maximal subgroup of | #14730392, #14730403, #14730480, … |
| maximal normal subgroup of | #14730392, #14730403, #14730480, … |
| maximal quotient of | #14913988, #14914486, #14914516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18558);