Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16837631 |
| Fitting | C23×C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#465 |
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 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.
1900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28488196, #28488198, #28488223, … |
| maximal normal subgroup of | #28488196, #28488198, #28488223, … |
| maximal quotient of | C2×#21423437, C2×#21423471, C2×#21423505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14070);