Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1746 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C22×C43 | C2×C42 |
| Fitting | C2×C4×C8×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C2×C4×C8 | D43 |
| hypocenter | C43 | #1746 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×C8 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,c^b=cg,h^b=h^421400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983442, #24983444, #24987052, … |
| maximal normal subgroup of | #24983442, #24983444, #24987052, … |
| maximal quotient of | #24987023, #24987026, #24987029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4261);