Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#66883 |
| Sylow | C11 ⋊ C22×#108 |
480 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 309 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 | #14659657, #14659659, #14659662, … |
| maximal normal subgroup of | #14659657, #14659659, #14659662, … |
| maximal quotient of | C22×#10622095, C22×#10622096, C2×#13067364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13113);