Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×M16×C43 ⋊ C2 |
| Sylow | C43 ⋊ #2922 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D43 |
| commutator, socle | C22×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C4×M16×C43 | C2 |
| hypercenter | C4×M16 | D43 |
| hypocenter | C43 | #2922 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C42 ◁ C4×M16 | |
400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 181 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,c^2=e,f^2=g,b^a=be,h^a=h^42,d^b=dg,h^b=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | #24987285, #24987290, #24987295, … |
| maximal normal subgroup of | #24987285, #24987290, #24987295, … |
| maximal quotient of | #25094083, C4×#14582867, C4×#14582927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13155);