Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#131×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2931 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C2×#131×C59 | C2 |
| hypercenter | C2×#131 | D59 |
| hypocenter | C59 | #2931 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C2×#131 | |
500 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,d^b=dg,h^b=h^581216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28497997, #28503884, #28504711, … |
| maximal normal subgroup of | #28497997, #28503884, #28504711, … |
| maximal quotient of | #28559203, #28559210, #28559212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13220);