Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Fitting | C43×#498 ⋊ C2 |
| Sylow | C43 ⋊ #1708 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063321 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#498 | C2 |
| socle | C22×C43 | #127 |
| hypercenter | #498 | D43 |
| hypocenter | C43 | #1708 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #498 | |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^2=d,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^42,h^c=h^42500 conjugacy classes — view the full character table.
| maximal subgroup of | #25010360, D43×#1708, C2×#19134197, … |
| maximal normal subgroup of | #25010360, D43×#1708, C2×#19134197, … |
| maximal quotient of | #24990369, #24996333, #24996335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4112);