Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2503 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C22×C4⋊C4×C43 | C2 |
| hypercenter | C22×C4⋊C4 | D43 |
| hypocenter | C43 | #2503 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^42878 conjugacy classes — view the full character table.
| maximal subgroup of | #24994319, #24994321, #24997063, … |
| maximal normal subgroup of | #24994319, #24994321, #24997063, … |
| maximal quotient of | #25018585, #25018828, #25019424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 8991);