Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D43 |
| commutator | C2×C43 | C22×C42 |
| Fitting | C4×#41×C43 | C2 |
| socle | C22×C43 | C23×C4 |
| hypercenter | C4×#41 | D43 |
| hypocenter | C43 | #2875 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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=e,b^2=f,e^2=g,b^a=bg,h^a=h^42,d^c=dg908 conjugacy classes — view the full character table.
| maximal subgroup of | #24993406, #24993410, #24993413, … |
| maximal normal subgroup of | #24993406, #24993410, #24993413, … |
| maximal quotient of | #25062190, #25062211, #25062273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12938);