Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×#497 ⋊ C2 |
| Sylow | C43 ⋊ #1661 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063293 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#497 | C2 |
| socle | C22×C43 | #120 |
| hypercenter | #497 | D43 |
| hypocenter | C43 | #1661 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #497 | |
208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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=g,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,d^c=dg,e^c=efg,h^c=h^42356 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1661, C2×#19133909, #25077747, … |
| maximal normal subgroup of | D43×#1661, C2×#19133909, #25077747, … |
| maximal quotient of | #24985392, #24985399, #24985416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3824);