Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C43 · Schur multiplier (H2) = C25×C4 |
| direct product | C43×#3027 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C43 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C22×C4×C43 ◁ G | |
772 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1247 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#13350, C43×#13351, C43×#13353, … |
| maximal normal subgroup of | C43×#13350, C43×#13351, C43×#13353, … |
| maximal quotient of | C43×#18300, C43×#18301, C43×#18302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 1759);