Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C43 · Schur multiplier (H2) = C22 |
| direct product | C43×#2069 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C23×C43 |
| prime radical | C22×D4×C43 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C22×C4×C43 ◁ G | |
216 conjugacy classes of subgroups.
989 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C43×#2069, C43×#23622, C43×#24808, … |
| maximal normal subgroup of | C2×C43×#2069, C43×#23622, C43×#24808, … |
| maximal quotient of | C43×#10603, C43×#10605, C43×#10607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 801);