Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C43 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×#41×C43 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C43 | C22 |
| commutator | C2 | C24×C4×C43 |
| Frattini, cosocle | C22 | C25×C43 |
| socle | C23×C43 | C24 |
| prime radical | C22×#41×C43 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C43 ◁ G | |
1728 conjugacy classes of subgroups.
3440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#8312, C43×#10758, C43×#10772, … |
| maximal normal subgroup of | C43×#8312, C43×#10758, C43×#10772, … |
| maximal quotient of | C2×C4×#117×C43, C2×C42×D4×C43, C2×C42×Q8×C43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2156);