Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #2112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D59 |
| commutator, socle | C22×C59 | C22×C8 |
| Fitting | C23×C8×C59 | C2 |
| hypercenter | C23×C8 | D59 |
| hypocenter | C59 | #2112 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C23×C8 | |
260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475641, #28475642, #28475643, … |
| maximal normal subgroup of | #28475641, #28475642, #28475643, … |
| maximal quotient of | #28497751, #28497823, #28497891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6121);