Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#494 ⋊ C2 |
| Sylow | C43 ⋊ D4×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#494 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #494 | D43 |
| hypocenter | C43 | D4×Q16 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #494 | |
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^42,h^c=h^42,e^d=eg,h^d=h^42497 conjugacy classes — view the full character table.
| maximal subgroup of | #25010032, #25010036, #25010060, … |
| maximal normal subgroup of | #25010032, #25010036, #25010060, … |
| maximal quotient of | #25086783, #25086798, #25086813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16260);