Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#391 ⋊ C2 |
| Sylow | C59 ⋊ #2855 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#391 | C2 |
| hypercenter | #391 | D59 |
| hypocenter | C59 | #2855 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #391 | |
564 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^58,h^b=h^58,h^c=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | #28477025, #28477051, #28477117, … |
| maximal normal subgroup of | #28477025, #28477051, #28477117, … |
| maximal quotient of | #28519872, #28519909, #28519934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12851);