Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C43 · Schur multiplier (H2) = C23 |
| direct product | C43×#1604 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C43 |
| prime radical | C43×#537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G | |
282 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
989 conjugacy classes — view the full character table.
| maximal subgroup of | C43×#12126, C43×#12128, C43×#12129, … |
| maximal normal subgroup of | C43×#12126, C43×#12128, C43×#12129, … |
| maximal quotient of | C43×#7752, C43×#7754, C43×#7764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 336);