Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×#41×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator | C2×C59 | C24×C4 |
| Frattini | C22 | C24×D59 |
| Fitting | C4×#41×C59 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | C4×#41 | D59 |
| hypocenter | C59 | #3428 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^d=h^581228 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28586416, #28586419, #28588234, … |
| maximal normal subgroup of | #28586416, #28586419, #28588234, … |
| maximal quotient of | #28746901, #28746916, #28746918, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17709);