Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C43 · Schur multiplier (H2) = C2×C4 |
| direct product | C43×#1564 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C43 | D4 |
| commutator | C4 | C22×C8×C43 |
| Frattini, cosocle | C42 | C23×C43 |
| socle | C22×C43 | C2×C4⋊C4 |
| prime radical | C23×C43 | C4⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C43 ◁ C2×C42×C43 ◁ G | |
180 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#7155, C43×#7157, C43×#7158, … |
| maximal normal subgroup of | C43×#7155, C43×#7157, C43×#7158, … |
| maximal quotient of | C43×#7872, C4×C43×#334, C4×C43×#335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 296);