Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10622295 |
| Sylow | C11 ⋊ C2×#500 |
424 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14649028, #14649030, #14652995, … |
| maximal normal subgroup of | #14649028, #14649030, #14652995, … |
| maximal quotient of | C2×#13068776, C2×#13069349, C2×#13069577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15018);