Finite Group DatabasebetaFinite Group Databasebeta| order | 5144 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5136 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C643 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C22×C643 |
| socle | C22×C643 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
5144 conjugacy classes. The character table is too large to display.
| center of | #97×C643, C22⋊C8×C643, C4⋊C8×C643, … |
| maximal subgroup of | C2×C3×C4×C643, C2×C4×C5×C643 |
| maximal normal subgroup of | C2×C3×C4×C643, C2×C4×C5×C643 |
| maximal quotient of | C2×C3×C4×C643, C2×C4×C5×C643 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5144, 2);