Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C11×#398 ⋊ C2 |
| Sylow | C11 ⋊ #2781 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C11×#398 | C2 |
| prime radical | C22×D44 | C22 |
| hypercenter | #398 | D11 |
| hypocenter | C11 | #2781 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #398 | |
434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=fg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,h^a=h^10,c^b=cg,d^b=de,h^b=h^10,h^c=h^10142 conjugacy classes — view the full character table.
| maximal subgroup of | #14961632, #14961647, #14961890, … |
| maximal normal subgroup of | #14961632, #14961647, #14961890, … |
| maximal quotient of | #14681583, #14681658, #14681673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12179);