Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #1749 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C22×C43 | C2×C42 |
| Fitting | C22×C42×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C22×C42 | D43 |
| hypocenter | C43 | #1749 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 | |
412 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 412 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:
2^7,43|a^2=e,b^2=f,c^2=e,f^2=g,b^a=bd,c^b=cg,h^b=h^421400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983136, #24983137, #24983169, … |
| maximal normal subgroup of | #24983136, #24983137, #24983169, … |
| maximal quotient of | #24987070, #24987080, #24987107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4272);