Finite Group DatabasebetaFinite Group Databasebeta| order | 5644 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C16×C41 (order 2624) · Inn(G) = C1 · Out(G) = C22×C16×C41 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C5644 |
| abelian | C4×C17×C83 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C2×C17×C83 |
| socle | C2×C17×C83 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
5644 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C4×C17×C83, Dic3×C17×C83, C4×C5×C17×C83, … |
| maximal normal subgroup of | C3×C4×C17×C83, C4×C5×C17×C83, C8×C17×C83, … |
| maximal quotient of | C3×C4×C17×C83, Dic3×C17×C83, C4×C5×C17×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5644, 1);