Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C23×C4 |
| Fitting | C43×#408 | C2 |
| hypercenter | #408 | D43 |
| hypocenter | C43 | #2923 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #408 | |
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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,c^2=e,f^2=g,b^a=be,c^a=cg,d^b=dg,h^c=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | #25006034, #25012879, #25012880, … |
| maximal normal subgroup of | #25006034, #25012879, #25012880, … |
| maximal quotient of | #25094085, #25094134, #25094490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13157);