Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×#41×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3498 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C4×#41×C43 | C2 |
| hypercenter | C4×#41 | D43 |
| hypocenter | C43 | #3498 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
1748 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1748 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^42,d^b=df884 conjugacy classes — view the full character table.
| maximal subgroup of | #24988505, #24988509, #24988813, … |
| maximal normal subgroup of | #24988505, #24988509, #24988813, … |
| maximal quotient of | #25256701, #25256974, #25257002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 18288);