Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C4×#4314 |
| Fitting | C2×C4×C8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14648333, #14648335, #14648354, … |
| maximal normal subgroup of | #14648333, #14648335, #14648354, … |
| maximal quotient of | C2×C8×#4314, C2×#13067461, C2×#13067454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13269);