Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#10622836 |
| Fitting | C23×D4×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D11 |
| commutator, cosocle | C23×C11 | C24 |
| Frattini | C23 | C23×D11 |
| Fitting | C23×D4×C11 | C2 |
| socle | C24×C11 | C23 |
| hypercenter | C23×D4 | D11 |
| hypocenter | C11 | C2×#392 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | #14648779, #14648794, #14653966, … |
| maximal normal subgroup of | #14648779, #14648794, #14653966, … |
| maximal quotient of | C2×#13066855, C2×#13066857, C2×#13066858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7705);