Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #525×D59 |
| Fitting | C59×#525 ⋊ C2 |
| Sylow | C59 ⋊ C2×#525 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C59×#525 | C2 |
| hypercenter | #525 | D59 |
| hypocenter | C59 | C2×#525 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
1880 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1501, D59×#1504, #28555849, … |
| maximal normal subgroup of | D59×#1501, D59×#1504, #28555849, … |
| maximal quotient of | D59×#2280, D59×#2290, D59×#2296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17746);