Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×C11⋊C32 |
| derived, Sylow | C11 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D11 |
| commutator, hypocenter | C11 | C4×C32 |
| Frattini | C2×C16 | C2×D11 |
| Fitting | C4×C11×C16 | C2 |
| socle, prime radical | C22×C11 | C2×C16 |
| cosocle | C2×C11×C16 | C22 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C4×C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C11⋊C8, C8×C11⋊C32, #14641100, … |
| maximal normal subgroup of | C32×C11⋊C8, C8×C11⋊C32, #14641100, … |
| maximal quotient of | C8×C11⋊C32, #14641104, #14641460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2642);