Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C11×#554 ⋊ C2 |
| Sylow | C11 ⋊ #3536 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C11×#554 | C2 |
| hypercenter | #554 | D11 |
| hypocenter | C11 | #3536 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #554 | |
1134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|e^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^c=h^10,h^d=h^10163 conjugacy classes — view the full character table.
| maximal subgroup of | #15639607, #15639609, #15639614, … |
| maximal normal subgroup of | #15639607, #15639609, #15639614, … |
| maximal quotient of | #14916544, #14916739, #14916743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18738);