Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #2183 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D59 |
| commutator, socle | C22×C59 | C22×C8 |
| Fitting | C59×C4⋊C16 | C2 |
| hypercenter | C4⋊C16 | D59 |
| hypocenter | C59 | #2183 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C4⋊C16 | |
126 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 69 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,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^b=h^58,h^c=h^581216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#2183, C2×#21426003, #28742178, … |
| maximal normal subgroup of | D59×#2183, C2×#21426003, #28742178, … |
| maximal quotient of | #28504035, #28504042, #28504046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6417);