Finite Group DatabasebetaFinite Group Databasebeta| order | 10026 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 26688 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3 |
| abelian | C2×C32×C557 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
10026 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C4×C557, C3⋊Dic1671, C3⋊Dic3×C557, … |
| maximal normal subgroup of | C32×C4×C557, C3⋊Dic1671, C3⋊Dic3×C557, … |
| maximal quotient of | C32×C4×C557, C22×C32×C557, C2×C3×C9×C557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10026, 5);