Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | #392×D59 |
| Fitting | C59×#392 ⋊ C2 |
| Sylow | C59 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#392 | C2 |
| hypercenter | #392 | D59 |
| hypocenter | C59 | C2×#392 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #392 | |
1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
682 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1343, #28499343, D59×#1595, … |
| maximal normal subgroup of | D59×#1343, #28499343, D59×#1595, … |
| maximal quotient of | D59×#1438, D59×#1439, D59×#1444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7704);