Finite Group DatabasebetaFinite Group Databasebeta| order | 12492 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C9×C347 |
| multiplicative | (ℤ/18741)ˣ, (ℤ/24988)ˣ, (ℤ/37482)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C3×C347 |
| socle, prime radical | C22×C3×C347 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
30 conjugacy classes of subgroups.
12492 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×C9×C347, C23×C9×C347 |
| maximal normal subgroup of | C2×C4×C9×C347, C23×C9×C347 |
| maximal quotient of | C2×C4×C9×C347, C23×C9×C347 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12492, 5);