Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2347 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#380 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #380 | D43 |
| hypocenter | C43 | #2347 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #380 | |
504 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 193 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=ef,c^2=e,d^2=e,b^a=be,c^a=cf,h^a=h^42,d^b=de,h^b=h^42638 conjugacy classes — view the full character table.
| maximal subgroup of | #24993764, #24993768, #24993792, … |
| maximal normal subgroup of | #24993764, #24993768, #24993792, … |
| maximal quotient of | #25018024, #25018051, #25018087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7405);