Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#504 ⋊ C2 |
| Sylow | C59 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D59 |
| commutator, socle | C2×C59 | C23×C8 |
| Fitting | C59×#504 | C2 |
| hypercenter | #504 | D59 |
| hypocenter | C59 | #3407 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C8 ◁ #504 | |
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 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,d^a=dg,c^b=cg,h^d=h^581228 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28741932, #28741935, #28741939, … |
| maximal normal subgroup of | #28741932, #28741935, #28741939, … |
| maximal quotient of | #28741327, #28741337, #28741338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17611);