Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #1817 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C22×C43 | C22×C8 |
| Fitting | C22×C42×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C22×C42 | D43 |
| hypocenter | C43 | #1817 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 | |
380 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 149 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=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^421400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983128, #24983129, #24983137, … |
| maximal normal subgroup of | #24983128, #24983129, #24983137, … |
| maximal quotient of | #24989920, #24989923, #24989926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4578);