Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ #1375 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic59 |
| commutator | C4×C59 | C4×C8 |
| Frattini | C22×C8 | C2×D59 |
| Fitting | C2×#97×C59 | C2 |
| socle | C22×C59 | #97 |
| hypercenter | C2×#97 | D59 |
| hypocenter | C59 | #1375 |
| LCS | G ▷ C4×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 | |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,e^a=eg,h^a=h^58,d^b=dg1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475446, #28475447, #28475466, … |
| maximal normal subgroup of | #28475446, #28475447, #28475466, … |
| maximal quotient of | #28475519, #28475531, #28475538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2590);