Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C3×C82×C13 (order 4992) · Inn(G) = C1 · Out(G) = C2×C3×C82×C13 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10016 |
| abelian | C32×C313 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C2×C313 |
| socle, prime radical | C2×C313 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
10016 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×C313, C2×C32×C313, M64×C313, … |
| maximal normal subgroup of | C64×C313, C2×C32×C313, M64×C313, … |
| maximal quotient of | C64×C313, C2×C32×C313, C3×C32×C313 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 1);