Finite Group DatabasebetaFinite Group Databasebeta| order | 10012 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C9×C139 (order 5004) · Inn(G) = C1 · Out(G) = C22×C9×C139 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10012 |
| abelian | C4×C2503 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C2×C2503 |
| socle, prime radical | C2×C2503 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6 conjugacy classes of subgroups.
10012 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C4×C2503⋊C3 |
| maximal subgroup of | C8×C2503, C2×C4×C2503, D4×C2503, … |
| maximal normal subgroup of | C8×C2503, C2×C4×C2503, D4×C2503, … |
| maximal quotient of | C8×C2503, C2×C4×C2503, C3×C4×C2503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10012, 2);