Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16837401 |
| Fitting | C22×C4⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#417 |
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28494164, #28494166, #28494207, … |
| maximal normal subgroup of | #28494164, #28494166, #28494207, … |
| maximal quotient of | C2×#21422481, C2×#21422533, #28555148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13020);