Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×(C2×D11)⋊C4 |
| Fitting | C2×C4×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ Q8×C22⋊C4 |
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14769486, #14769487, #14769516, … |
| maximal normal subgroup of | #14769486, #14769487, #14769516, … |
| maximal quotient of | C4⋊C4×(C2×D11)⋊C4, Q8×C11⋊#95, #14675314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7343);