Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #1444 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D11 |
| commutator | C23×C11 | C22×C4 |
| Fitting | C2×C11×#95 | C2 |
| socle, prime radical, cosocle | C24×C11 | C23 |
| hypercenter | C2×#95 | D11 |
| hypocenter | C11 | #1444 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
608 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=d,c^2=e,b^a=bd,c^a=ce,c^b=cf,h^b=h^10,h^c=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14640569, #14640571, #14647821, … |
| maximal normal subgroup of | #14640569, #14640571, #14647821, … |
| maximal quotient of | #14641699, #14641701, #14662376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2774);