Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C43⋊#1308 |
| Sylow | C43 ⋊ #1308 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C43⋊#95 |
| commutator | C23×C43 | C42 |
| Frattini | C2×C42 | C2×D43 |
| Fitting | C43×#432 | C2 |
| socle | C22×C43 | #95 |
| hypercenter | #432 | D43 |
| hypocenter | C43 | #1308 |
| LCS | G ▷ C23×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #432 | |
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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=d,b^2=e,d^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^42614 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1308, C2×C43⋊#1308, #24986999, … |
| maximal normal subgroup of | D43×#1308, C2×C43⋊#1308, #24986999, … |
| maximal quotient of | #24983169, #24983170, #24983171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2422);