Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1723 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063321 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#487 | C2 |
| socle | C22×C43 | #127 |
| hypercenter | #487 | D43 |
| hypocenter | C43 | #1723 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #487 | |
176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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=g,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^42,c^b=cf,h^b=h^42,h^c=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1723, C2×#19134275, #25084399, … |
| maximal normal subgroup of | D43×#1723, C2×#19134275, #25084399, … |
| maximal quotient of | #24990388, #24996416, #24996417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4190);