Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C43 · Schur multiplier (H2) = C22 |
| direct product | C43×#1451 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C43 | C23 |
| commutator | C22 | C2×C42×C43 |
| Frattini, cosocle | C42 | C23×C43 |
| socle | C22×C43 | C2×C42 |
| prime radical | C23×C43 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C43 ◁ G | |
208 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 152 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×#7164, C43×#7166, C43×#7210, … |
| maximal normal subgroup of | C43×#7164, C43×#7166, C43×#7210, … |
| maximal quotient of | C43×#7842, C43×#7848, C43×#8132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 183);