Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C43×#380 ⋊ C2 |
| Sylow | C43 ⋊ D4×C22⋊C4 |
| 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 | D4×C22⋊C4 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #380 | |
1252 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 253 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^a=be,c^a=cf,d^b=de,h^b=h^42,h^d=h^42638 conjugacy classes — view the full character table.
| maximal subgroup of | #24993013, #24993017, #24993041, … |
| maximal normal subgroup of | #24993013, #24993017, #24993041, … |
| maximal quotient of | #25017996, #25018016, #25018066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7330);