Finite Group DatabasebetaFinite Group Databasebeta| order | 12492 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C12492 |
| abelian | C4×C9×C347 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C2×C3×C347 |
| socle, prime radical | C2×C3×C347 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
18 conjugacy classes of subgroups.
12492 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic12492, D24984 |
| maximal subgroup of | C8×C9×C347, C2×C4×C9×C347, Dic6246, … |
| maximal normal subgroup of | C8×C9×C347, C2×C4×C9×C347, Dic6246, … |
| maximal quotient of | C8×C9×C347, C2×C4×C9×C347 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12492, 1);