Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×Dic236 |
| Sylow | C59 ⋊ Q8×Q16 |
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1195 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28502377, #28502381, #28502405, … |
| maximal normal subgroup of | #28502377, #28502381, #28502405, … |
| maximal quotient of | Q8×#14273652, C4⋊C4×Dic236, Q8×#14273661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17395);