Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C43 · Schur multiplier (H2) = C23 |
| direct product | C43×#2195 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C43 |
| prime radical | C43×#578 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C2×C4×C43 ◁ #131×C43 ◁ G | |
206 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
989 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C43×#2195, C43×#33538, C43×#33540, … |
| maximal normal subgroup of | C2×C43×#2195, C43×#33538, C43×#33540, … |
| maximal quotient of | C43×#12112, C43×#12113, C43×#12168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 927);