Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C59 ⋊ Q8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#384 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #384 | D59 |
| hypocenter | C59 | Q8×C4⋊C4 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #384 | |
568 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^d=h^58862 conjugacy classes — view the full character table.
| maximal subgroup of | #28482860, #28482864, #28482888, … |
| maximal normal subgroup of | #28482860, #28482864, #28482888, … |
| maximal quotient of | #28510125, #28510129, #28510173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7422);