Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C43 · Schur multiplier (H2) = C25 |
| direct product | C2×C43×#401 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C43 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C43 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C43 ◁ G | |
516 conjugacy classes of subgroups.
1892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C43×#401, C43×#14251, C43×#14333, … |
| maximal normal subgroup of | C4×C43×#401, C43×#14251, C43×#14333, … |
| maximal quotient of | C2×C43×#1443, C4×C43×#401, C43×C22⋊#401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 1132);