Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#575 ⋊ C2 |
| Sylow | C43 ⋊ #2017 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063321 |
| commutator | C22×C4×C43 | C23 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#575 | C2 |
| socle | C2×C43 | #392 |
| hypercenter | #575 | D43 |
| hypocenter | C43 | #2017 |
| LCS | G ▷ C22×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,f^b=fg,e^c=eg,f^c=fg,h^c=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | #25008777, #25008782, #25008787, … |
| maximal normal subgroup of | #25008777, #25008782, #25008787, … |
| maximal quotient of | #24997194, #24997195, #24997199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5613);