Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C43×#413 ⋊ C2 |
| Sylow | C43 ⋊ #3018 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063295 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#413 | C2 |
| socle | C2×C43 | C2×#120 |
| hypercenter | #413 | D43 |
| hypocenter | C43 | #3018 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #413 | |
724 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^42,e^b=eg,f^b=fg,h^b=h^42,e^c=eg494 conjugacy classes — view the full character table.
| maximal subgroup of | #25013918, #25013923, #25013928, … |
| maximal normal subgroup of | #25013918, #25013923, #25013928, … |
| maximal quotient of | #25068707, #25068758, #25068809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13863);