Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C59×#380 ⋊ C2 |
| Sylow | C59 ⋊ #2703 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#380 | C2 |
| hypercenter | #380 | D59 |
| hypocenter | C59 | #2703 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #380 | |
612 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^58,c^b=cg,d^b=de844 conjugacy classes — view the full character table.
| maximal subgroup of | #28795650, #28795653, #28795745, … |
| maximal normal subgroup of | #28795650, #28795653, #28795745, … |
| maximal quotient of | #28516021, #28516148, #28516224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 11153);