Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C43 · Schur multiplier (H2) = C25 |
| direct product | C43×#3358 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C43 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C4×Q8×C43 ◁ G | |
426 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1505 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#19756, C43×#19760, C43×#19761, … |
| maximal normal subgroup of | C43×#19756, C43×#19760, C43×#19761, … |
| maximal quotient of | Q8×#102×C43, C43×#22540, C43×#22740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2090);