Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #391×D59 |
| Fitting | C59×#391 ⋊ C2 |
| Sylow | C59 ⋊ C2×#391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#391 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #391 | D59 |
| hypocenter | C59 | C2×#391 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #391 | |
928 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1272, #28476685, #28476776, … |
| maximal normal subgroup of | D59×#1272, #28476685, #28476776, … |
| maximal quotient of | D59×C4⋊#95, D59×#1436, #28509887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6976);