Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#14273720 |
| Sylow | C59 ⋊ C4×#126 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C22×C59 | C23×C4 |
| Frattini | C23 | C23×D59 |
| Fitting | C4×C22⋊C4×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C4×C22⋊C4 | D59 |
| hypocenter | C59 | C4×#126 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
516 conjugacy classes of subgroups.
1216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14273720, #28596905, #28596907, … |
| maximal normal subgroup of | C8×#14273720, #28596905, #28596907, … |
| maximal quotient of | C4×#16837290, C4×#16837295, C4×#16837296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7059);