Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C43 · Schur multiplier (H2) = C24 |
| direct product | C2×C43×#341 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C43 | D4 |
| commutator | C4 | C2×C42×C43 |
| Frattini, cosocle | C22×C4 | C23×C43 |
| socle | C23×C43 | C4⋊C4 |
| prime radical | C24×C43 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C43 ◁ C23×C4×C43 ◁ G | |
392 conjugacy classes of subgroups.
2408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#7259, C43×#7261, C43×#7263, … |
| maximal normal subgroup of | C43×#7259, C43×#7261, C43×#7263, … |
| maximal quotient of | C2×C43×#1277, C43×#7872, C43×#7874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 469);