Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C43 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C43×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C43 | C22 |
| commutator | C2 | C22×C42×C43 |
| Frattini, cosocle | C2×C4 | C24×C43 |
| socle | C23×C43 | C22×C4 |
| prime radical | C24×C43 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C43 ◁ G | |
592 conjugacy classes of subgroups.
3440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#8156, C43×#8157, C43×#8601, … |
| maximal normal subgroup of | C43×#8156, C43×#8157, C43×#8601, … |
| maximal quotient of | C2×C8×M16×C43, C2×C43×#1450, C2×C43×#1451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 1604);