Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2342 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator | C22×C11 | C23×C4 |
| Fitting | C11×#379 | C2 |
| socle, cosocle | C23×C11 | C24 |
| prime radical | C25×C11 | C22 |
| hypercenter | #379 | D11 |
| hypocenter | C11 | #2342 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #379 | |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=f,b^a=be,c^a=cf,h^a=h^10,d^b=de,h^b=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | #14769104, #14769108, #14769912, … |
| maximal normal subgroup of | #14769104, #14769108, #14769912, … |
| maximal quotient of | #14675176, #14675181, #14675205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7361);