Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C43 · Schur multiplier (H2) = C214 |
| direct product | C24×Q8×C43 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C43 | C22 |
| commutator, Frattini, cosocle | C2 | C26×C43 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25×C43 ◁ G | |
6264 conjugacy classes of subgroups.
3440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×#1446, C43×#13922, C43×#14336, … |
| maximal normal subgroup of | C2×C43×#1446, C43×#13922, C43×#14336, … |
| maximal quotient of | C24×C4⋊C4×C43, C23×C4×Q8×C43, C23×C22⋊Q8×C43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2321);