Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 628992 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C13 |
| abelian | C3×C4×C7×C132 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C2×C3×C7×C132 |
| socle, prime radical | C2×C3×C7×C132 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
14196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×C8×C132, C2×C3×C4×C7×C132 |
| maximal normal subgroup of | C3×C7×C8×C132, C2×C3×C4×C7×C132 |
| maximal quotient of | C3×C7×C8×C132, C2×C3×C4×C7×C132 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 77);