Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2396 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator, socle | C23×C59 | C24 |
| Frattini | C23 | C23×D59 |
| Fitting | C4×C4⋊C4×C59 | C2 |
| hypercenter | C4×C4⋊C4 | D59 |
| hypocenter | C59 | #2396 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
528 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^58,h^c=h^581204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28483777, #28483782, #28560969, … |
| maximal normal subgroup of | #28483777, #28483782, #28560969, … |
| maximal quotient of | #28510402, #28510416, #28510434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7782);