Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #1767 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator | C22×C59 | C2×C42 |
| Fitting | C43×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C43 | D59 |
| hypocenter | C59 | #1767 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
292 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 165 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=f,c^2=de,f^2=g,b^a=bd,c^b=cg,h^b=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475231, #28475232, #28475245, … |
| maximal normal subgroup of | #28475231, #28475232, #28475245, … |
| maximal quotient of | #28479818, #28479828, #28479851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4363);