Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C43 · Schur multiplier (H2) = C2×C8 |
| direct product | C43×#1709 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C43 |
| prime radical | C43×#493 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C42×C43 ◁ G | |
212 conjugacy classes of subgroups.
1634 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#7092, C43×#7530, C43×#7531, … |
| maximal normal subgroup of | C43×#7092, C43×#7530, C43×#7531, … |
| maximal quotient of | C43×#8816, C43×#9822, C43×#9824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 441);