Finite Group DatabasebetaFinite Group Databasebeta| order | 5634 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C32×C8×C13 (order 1872) · Inn(G) = C1 · Out(G) = C2×C32×C8×C13 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C5634 |
| abelian | C2×C9×C313 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C3 | C2×C3×C313 |
| socle | C2×C3×C313 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
5634 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C9×C313, Dic9×C313, C9×Dic313, … |
| maximal normal subgroup of | C4×C9×C313, Dic9×C313, C9×Dic313, … |
| maximal quotient of | C4×C9×C313, C22×C9×C313, C2×C5×C9×C313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5634, 1);