Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C43×#336 ⋊ C2 |
| Sylow | C43 ⋊ #1798 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator, socle | C23×C43 | C22×C4 |
| Fitting | C43×#336 | C2 |
| hypercenter | #336 | D43 |
| hypocenter | C43 | #1798 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
312 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 101 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,b^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^b=h^42,h^c=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1798, C2×#19134578, #25095962, … |
| maximal normal subgroup of | D43×#1798, C2×#19134578, #25095962, … |
| maximal quotient of | #24989269, #24989274, #24989299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4493);