Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9984 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C16×C313 |
| multiplicative | (ℤ/15027)ˣ, (ℤ/20036)ˣ, (ℤ/30054)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C22×C313 |
| socle, prime radical | C22×C313 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
28 conjugacy classes of subgroups.
10016 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C16×C313, #346×C313, C22⋊C16×C313, … |
| maximal normal subgroup of | C4×C16×C313, #346×C313, C22⋊C16×C313, … |
| maximal quotient of | C4×C16×C313, C22⋊C16×C313, C4⋊C16×C313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 16);