Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1564 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22⋊D43 |
| commutator | C4×C43 | C22×C8 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#431 | C2 |
| socle | C22×C43 | C2×C4⋊C4 |
| hypercenter | #431 | D43 |
| hypocenter | C43 | #1564 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C42 ◁ C2×C42 ◁ #431 | |
180 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 101 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=e,b^2=d,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^b=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | #24987754, #24987756, #24987758, … |
| maximal normal subgroup of | #24987754, #24987756, #24987758, … |
| maximal quotient of | #24986055, C4×#14582649, C4×#14582651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3256);