Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #2420 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting, prime radical | C2×C11×#121 | C2 |
| hypercenter | C2×#121 | D11 |
| hypocenter | C11 | #2420 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
596 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | #14797521, #14797524, #14797536, … |
| maximal normal subgroup of | #14797521, #14797524, #14797536, … |
| maximal quotient of | #14675709, #14676106, #14676580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7998);