Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #557×D59 |
| Fitting | C59×#557 ⋊ C2 |
| Sylow | C59 ⋊ C2×#557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C59×#557 | C2 |
| hypercenter | #557 | D59 |
| hypocenter | C59 | C2×#557 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #557 | |
1048 conjugacy classes of subgroups.
775 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1626, D59×#1636, D59×#1648, … |
| maximal normal subgroup of | D59×#1626, D59×#1636, D59×#1648, … |
| maximal quotient of | Q8×C4⋊C4×D59, D59×#2351, D59×#2355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18078);