Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#430 ⋊ C2 |
| Sylow | C43 ⋊ #2916 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D43 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#430 | C2 |
| socle | C2×C43 | C22×C4⋊C4 |
| hypercenter | #430 | D43 |
| hypocenter | C43 | #2916 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #430 | |
440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 209 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=e,e^2=g,f^2=g,b^a=be,e^a=eg,h^b=h^42,d^c=dg,h^d=h^42506 conjugacy classes — view the full character table.
| maximal subgroup of | #25115115, #25115118, #25115123, … |
| maximal normal subgroup of | #25115115, #25115118, #25115123, … |
| maximal quotient of | #25065585, #25065590, #25065638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13120);