Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C43 · Schur multiplier (H2) = C29 |
| direct product | C4×2−1+4×C43 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C43 | C24 |
| commutator | C2 | C24×C4×C43 |
| Frattini, cosocle | C22 | C25×C43 |
| socle | C22×C43 | C25 |
| prime radical | C2×2−1+4×C43 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C43 ◁ G | |
1492 conjugacy classes of subgroups; only the 1372 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1372 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#8319, C43×#17439, C43×#17454, … |
| maximal normal subgroup of | C43×#8319, C43×#17439, C43×#17454, … |
| maximal quotient of | C4×C43×#520, C4×C43×#519, C4×C43×#536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2162);