Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator | C22×C11 | C23×C4 |
| Fitting, prime radical | C22×C11×#41 | C2 |
| socle, cosocle | C23×C11 | C24 |
| hypercenter | C22×#41 | D11 |
| hypocenter | C11 | #2311 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
880 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^10,c^b=ce244 conjugacy classes — view the full character table.
| maximal subgroup of | #14659101, #14659103, #14659166, … |
| maximal normal subgroup of | #14659101, #14659103, #14659166, … |
| maximal quotient of | #14675025, #14675075, #14675082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7102);