Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C4×C22⋊C4×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C4×C22⋊C4 | D59 |
| hypocenter | C59 | #2337 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^581204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#2337, C2×#21426904, #28747613, … |
| maximal normal subgroup of | D59×#2337, C2×#21426904, #28747613, … |
| maximal quotient of | #28509961, #28510018, #28510026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7318);