Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×#10623214 |
| Fitting | C2×C11×#124 ⋊ C2 |
| Sylow | C11 ⋊ C2×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D11 |
| commutator, cosocle | C22×C11 | C25 |
| Frattini | C22 | C24×D11 |
| Fitting | C2×C11×#124 | C2 |
| socle | C23×C11 | C24 |
| hypercenter | C2×#124 | D11 |
| hypocenter | C11 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
178 conjugacy classes — view the full character table.
| maximal subgroup of | #14646214, #14646215, #14669595, … |
| maximal normal subgroup of | #14646214, #14646215, #14669595, … |
| maximal quotient of | C2×#13071753, C2×#13071756, C2×#13071785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18630);