Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ #2163 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D59 |
| commutator, socle | C22×C59 | C22×C8 |
| Fitting | C2×C4×C8×C59 | C2 |
| hypercenter | C2×C4×C8 | D59 |
| hypocenter | C59 | #2163 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 | |
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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,c^2=d,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 | #28475532, #28475533, #28475534, … |
| maximal normal subgroup of | #28475532, #28475533, #28475534, … |
| maximal quotient of | #28503691, #28503720, #28503998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6313);