Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C43 · Schur multiplier (H2) = C22 |
| direct product | C43×#1387 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | #102 |
| commutator | C8 | C42×C43 |
| Frattini, cosocle | C22×C8 | C22×C43 |
| prime radical | C23×C43 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C22×C8×C43 ◁ G | |
136 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×#1387, C43×#12569, C4×C43×#361, … |
| maximal normal subgroup of | C2×C43×#1387, C43×#12569, C4×C43×#361, … |
| maximal quotient of | C43×#7159, C43×#7176, C43×#7178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 119);