Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #1374 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C8 | C2×D43 |
| commutator | C2×C43 | C4×C16 |
| Fitting | C2×C4×C8×C43 | C2 |
| socle | C23×C43 | C2×C8 |
| hypercenter | C2×C4×C8 | D43 |
| hypocenter | C43 | #1374 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C8 ◁ C2×C4×C8 | |
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 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=d,b^2=e,d^2=f,f^2=g,b^a=bc,h^a=h^421424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983340, #24983341, #24983363, … |
| maximal normal subgroup of | #24983340, #24983341, #24983363, … |
| maximal quotient of | #24983425, #24983439, #24983446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2588);