Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | #390×D59 |
| Fitting | C59×#390 ⋊ C2 |
| Sylow | C59 ⋊ C2×#390 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#390 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #390 | D59 |
| hypocenter | C59 | C2×#390 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #390 | |
1360 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1270, #28476672, #28476764, … |
| maximal normal subgroup of | D59×#1270, #28476672, #28476764, … |
| maximal quotient of | D59×C4⋊#95, D59×#1437, #28509872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6963);