Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C43 · Schur multiplier (H2) = C27 |
| direct product | C4×#120×C43 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C43 | C23 |
| commutator | C22 | C23×C4×C43 |
| Frattini, cosocle | C23 | C24×C43 |
| socle | C23×C43 | C24 |
| prime radical | C2×#120×C43 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C43 ◁ G | |
1224 conjugacy classes of subgroups; only the 368 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 368 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×#8965, C43×#8967, C43×#11471, … |
| maximal normal subgroup of | C43×#8965, C43×#8967, C43×#11471, … |
| maximal quotient of | C4×C43×#386, C4×C43×#385, C4×C43×#379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 1031);