Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C43×#453 ⋊ C2 |
| Sylow | C43 ⋊ #3019 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #120×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#453 | C2 |
| socle | C2×C43 | C2×#120 |
| hypercenter | #453 | D43 |
| hypocenter | C43 | #3019 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #453 | |
762 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 762 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|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^d=h^42365 conjugacy classes — view the full character table.
| maximal subgroup of | #25250651, #25250657, #25250664, … |
| maximal normal subgroup of | #25250651, #25250657, #25250664, … |
| maximal quotient of | #25068964, #25068971, #25069007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13864);