Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×Dic59⋊C8 |
| Sylow | C59 ⋊ C4×C4⋊C8 |
316 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479809, C8×Dic59⋊C8, #28479813, … |
| maximal normal subgroup of | #28479809, C8×Dic59⋊C8, #28479813, … |
| maximal quotient of | C8×Dic59⋊C8, #28479815, #28479824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4360);