Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C43 · Schur multiplier (H2) = C23×C4 |
| direct product | C43×#3206 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C43 |
| prime radical | C43×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G | |
428 conjugacy classes of subgroups.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#9267, C43×#9289, C43×#9301, … |
| maximal normal subgroup of | C43×#9267, C43×#9289, C43×#9301, … |
| maximal quotient of | C43×#21804, C43×#21859, C43×#21981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 1938);