Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C43 ⋊ #2880 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C23×C4 |
| Fitting | C22×#41×C43 | C2 |
| hypercenter | C22×#41 | D43 |
| hypocenter | C43 | #2880 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
774 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 297 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,f^2=g,b^a=be,h^a=h^42,d^c=dg890 conjugacy classes — view the full character table.
| maximal subgroup of | #24992902, #24992906, #24992916, … |
| maximal normal subgroup of | #24992902, #24992906, #24992916, … |
| maximal quotient of | #25062782, #25062792, #25062801, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12959);