Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C43 · Schur multiplier (H2) = C2 |
| direct product | C43×#2227 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C43 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C43 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C42×C43 ◁ C4×C8×C43 ◁ G | |
130 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 130 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.
1247 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#12373, C43×#12374, C43×#12379, … |
| maximal normal subgroup of | C43×#12373, C43×#12374, C43×#12379, … |
| maximal quotient of | C43×#12812, C43×#12936, C43×#13112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 959);