Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C43 · Schur multiplier (H2) = C2×C4 |
| direct product | C43×#1408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | #353 |
| commutator | C42 | C2×C4×C43 |
| Frattini, cosocle | #127 | C22×C43 |
| prime radical | C43×#493 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C22×C43 ◁ C2×C4×C43 ◁ #127×C43 ◁ G | |
120 conjugacy classes of subgroups.
731 conjugacy classes — view the full character table.
| maximal subgroup of | C43×#7515, C43×#7516, C43×#7529, … |
| maximal normal subgroup of | C43×#7515, C43×#7516, C43×#7529, … |
| maximal quotient of | C43×#7354, C43×#7370, C43×#7402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 140);