Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C11×#568 ⋊ C2 |
| Sylow | C11 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D11 |
| commutator, socle | C2×C11 | C24×C4 |
| Fitting | C11×#568 | C2 |
| prime radical | #10623453 | C2 |
| cosocle | C4×C11 | C25 |
| hypercenter | #568 | D11 |
| hypocenter | C11 | #3573 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,f^2=g,h^a=h^10,e^b=eg,d^c=dg,h^e=h^10238 conjugacy classes — view the full character table.
| maximal subgroup of | #14759732, #14759734, #14759738, … |
| maximal normal subgroup of | #14759732, #14759734, #14759738, … |
| maximal quotient of | #15617195, #15617196, #15617197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 19223);