Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×#364 ⋊ C2 |
| Sylow | C43 ⋊ #2171 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D43 |
| commutator | C4×C43 | C22×C8 |
| Frattini | C2×C8 | C22×D43 |
| Fitting | C43×#364 | C2 |
| socle | C2×C43 | C8×D4 |
| hypercenter | #364 | D43 |
| hypocenter | C43 | #2171 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #364 | |
144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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=e,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,d^a=dg,d^b=dg,h^b=h^42,h^c=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | #25008484, #25008486, #25010999, … |
| maximal normal subgroup of | #25008484, #25008486, #25010999, … |
| maximal quotient of | #25008306, #25008369, #25008376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6351);