Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C43 · Schur multiplier (H2) = C24×C4 |
| direct product | C43×#2283 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C43 | C23 |
| commutator | C22 | C23×C4×C43 |
| Frattini, cosocle | C23 | C24×C43 |
| socle | C23×C43 | C24 |
| prime radical | C24×C43 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C43 ◁ G | |
568 conjugacy classes of subgroups.
2408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#7857, C43×#7858, C43×#7894, … |
| maximal normal subgroup of | C43×#7857, C43×#7858, C43×#7894, … |
| maximal quotient of | C43×#13753, C43×#13755, C43×#13757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 1015);