Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q82×D11 |
| Fitting | Q82×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | Q82×C11 | C2 |
| prime radical | C22×D11 | C24 |
| hypercenter | Q82 | D11 |
| hypocenter | C11 | C2×Q82 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1112 conjugacy classes of subgroups; only the 575 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 575 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1623, D11×#1633, D11×#1645, … |
| maximal normal subgroup of | D11×#1623, D11×#1633, D11×#1645, … |
| maximal quotient of | Q8×C4⋊C4×D11, D11×#2369, Q8×#66940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18084);