Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #41×D44 |
| Fitting | C4×C11×#41 ⋊ C2 |
| Sylow | C11 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Frattini | C22 | C24×D11 |
| Fitting | C4×C11×#41 | C2 |
| hypercenter | C4×#41 | D11 |
| hypocenter | C11 | D4×#41 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645794, #14645798, #14720630, … |
| maximal normal subgroup of | #14645794, #14645798, #14720630, … |
| maximal quotient of | #41×(C2×D11)⋊C4, #41×C4⋊Dic11, #117×D44, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18001);