Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ C8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C2×C43 | C2×C4×C8 |
| Fitting | C2×C4⋊C8×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D43 |
| hypocenter | C43 | C8×C4⋊C4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
296 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 165 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=f,c^2=de,e^2=g,b^a=bd,h^a=h^42,h^b=h^42,h^c=h^42920 conjugacy classes — view the full character table.
| maximal subgroup of | #24987358, #24987364, #24987365, … |
| maximal normal subgroup of | #24987358, #24987364, #24987365, … |
| maximal quotient of | C4⋊C8×C43⋊C8, #24987729, #24987746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4375);