Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #2166 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14273686 |
| commutator | C2×C4×C59 | C22×C4 |
| Frattini | C2×C8 | C22×D59 |
| Fitting | C59×#405 | C2 |
| socle | C2×C59 | #432 |
| hypercenter | #405 | D59 |
| hypocenter | C59 | #2166 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ #97 ◁ #405 | |
122 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^58,c^b=cg,e^b=eg,e^c=eg1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475783, #28475784, #28475785, … |
| maximal normal subgroup of | #28475783, #28475784, #28475785, … |
| maximal quotient of | #28503709, #28503759, #28504027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6326);