Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#342 ⋊ C2 |
| Sylow | C43 ⋊ #1799 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊C4×D43 |
| commutator | C23×C43 | C22×C4 |
| Frattini | C24 | C22×D43 |
| Fitting | C43×#342 | C2 |
| socle | C22×C43 | C2×C22⋊C4 |
| hypercenter | #342 | D43 |
| hypocenter | C43 | #1799 |
| LCS | G ▷ C23×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #342 | |
380 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 87 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=f,b^2=d,b^a=bd,c^a=ce,e^a=eg,h^b=h^42,f^c=fg,h^c=h^42494 conjugacy classes — view the full character table.
| maximal subgroup of | #25007355, #25007357, #25007360, … |
| maximal normal subgroup of | #25007355, #25007357, #25007360, … |
| maximal quotient of | #24989253, #24989257, #24989261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4497);