Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#385 ⋊ C2 |
| Sylow | C11 ⋊ #2782 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C11×#385 | C2 |
| prime radical | C22×C22⋊D11 | C22 |
| hypercenter | #385 | D11 |
| hypocenter | C11 | #2782 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #385 | |
448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=efg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^10,h^d=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14961610, #14961612, #14961615, … |
| maximal normal subgroup of | #14961610, #14961612, #14961615, … |
| maximal quotient of | #14681574, #14681580, #14682005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12185);