Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C43 · Schur multiplier (H2) = C22 |
| direct product | C43×#1283 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C43 | C22⋊C4 |
| commutator | C22 | C4×C8×C43 |
| Frattini, cosocle | C2×C42 | C22×C43 |
| socle | C22×C43 | #95 |
| prime radical | C23×C43 | C42 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G | |
160 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×#1283, C43×#7932, C43×#7933, … |
| maximal normal subgroup of | C2×C43×#1283, C43×#7932, C43×#7933, … |
| maximal quotient of | C43×#7016, C43×#7022, C43×#7023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15);