Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C43 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C43×#322 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C43 | C22 |
| commutator | C2 | C2×C4×C8×C43 |
| Frattini, cosocle | C42 | C23×C43 |
| socle, prime radical | C23×C43 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C43 ◁ G | |
248 conjugacy classes of subgroups.
3440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#7137, C43×#7139, C43×#7145, … |
| maximal normal subgroup of | C43×#7137, C43×#7139, C43×#7145, … |
| maximal quotient of | C4×C43×#322, C2×C43×#1273, C43×#8131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 180);