Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2164 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D43 |
| commutator, socle | C22×C43 | C22×C8 |
| Fitting | C43×C22⋊C16 | C2 |
| hypercenter | C22⋊C16 | D43 |
| hypocenter | C43 | #2164 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C22⋊C16 | |
138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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,c^2=d,e^2=f,f^2=g,b^a=bd,c^b=cg,h^c=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2164, C2×#19136399, #25249680, … |
| maximal normal subgroup of | D43×#2164, C2×#19136399, #25249680, … |
| maximal quotient of | #25011600, #25011634, #25011909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6314);