Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ #1953 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14273701 |
| commutator | C2×C4×C59 | C22×C4 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#405 | C2 |
| socle | C2×C59 | #389 |
| hypercenter | #405 | D59 |
| hypocenter | C59 | #1953 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #405 | |
184 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 89 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=f,b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^58,d^b=dg1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28505330, #28505333, #28505365, … |
| maximal normal subgroup of | #28505330, #28505333, #28505365, … |
| maximal quotient of | #28487300, #28487305, #28487310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5300);