Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#4341 |
| Fitting | D4×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | D4×Q8×C11 | C2 |
| prime radical | C2×#4341 | C22 |
| hypercenter | D4×Q8 | D11 |
| hypocenter | C11 | Q8×#41 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | #14729750, #14729758, #14729765, … |
| maximal normal subgroup of | #14729750, #14729758, #14729765, … |
| maximal quotient of | C4⋊C4×#4341, Q8×#66930, Q8×#66945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18087);