Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C43×#376 ⋊ C2 |
| Sylow | C43 ⋊ #2372 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#376 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #376 | D43 |
| hypocenter | C43 | #2372 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #376 | |
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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=eg,c^2=e,d^2=f,b^a=be,c^a=cf,d^b=de,h^b=h^42890 conjugacy classes — view the full character table.
| maximal subgroup of | #24994213, #24994215, #24994223, … |
| maximal normal subgroup of | #24994213, #24994215, #24994223, … |
| maximal quotient of | #25018049, #25018123, #25018128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7620);