Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | C4×#14273637 |
| Sylow | C59 ⋊ C4×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D59 |
| commutator | C2×C59 | C43 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C2×C4×C8×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C2×C4×C8 | D59 |
| hypocenter | C59 | C4×#97 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
360 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475546, C8×#14273637, #28478041, … |
| maximal normal subgroup of | #28475546, C8×#14273637, #28478041, … |
| maximal quotient of | C4×#16837123, C4×#16837124, C8×#14273637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4194);