Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C59×#520 ⋊ C2 |
| Sylow | C59 ⋊ C4×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator | C2×C59 | C24×C4 |
| Fitting | C59×#520 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | #520 | D59 |
| hypocenter | C59 | C4×2−1+4 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #520 | |
1492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=f,c^2=f,e^2=g,b^a=bf,d^a=df,c^b=cf,h^c=h^58,h^e=h^581054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28594582, #28594588, #28594593, … |
| maximal normal subgroup of | #28594582, #28594588, #28594593, … |
| maximal quotient of | #28746927, #28746930, #520×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17721);