Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #1867 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063295 |
| commutator | C23×C43 | C22×C4 |
| Frattini | C24 | C22×D43 |
| Fitting | C2×#99×C43 | C2 |
| socle | C22×C43 | #120 |
| hypercenter | C2×#99 | D43 |
| hypocenter | C43 | #1867 |
| LCS | G ▷ C23×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C2×#99 | |
374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^a=bd,c^a=ce,h^a=h^42,e^b=eg,h^b=h^42,d^c=dg494 conjugacy classes — view the full character table.
| maximal subgroup of | #25013352, #25013353, #25013359, … |
| maximal normal subgroup of | #25013352, #25013353, #25013359, … |
| maximal quotient of | #24990565, #24990570, #24990575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4793);