Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C43×#421 ⋊ C2 |
| Sylow | C43 ⋊ #1976 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063297 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#421 | C2 |
| socle | C2×C43 | #390 |
| hypercenter | #421 | D43 |
| hypocenter | C43 | #1976 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #421 | |
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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=f,b^2=df,c^2=e,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,f^b=fg,h^b=h^42,h^c=h^42494 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1976, C2×#19135492, #25100573, … |
| maximal normal subgroup of | D43×#1976, C2×#19135492, #25100573, … |
| maximal quotient of | #24995515, #24995519, #24995522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5407);