Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#10622446 |
| Fitting | C2×C11×C4⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14643230, #14643233, #14643251, … |
| maximal normal subgroup of | #14643230, #14643233, #14643251, … |
| maximal quotient of | C2×#13068360, C2×#13068373, C2×C4⋊C8×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13125);