Finite Group DatabasebetaFinite Group Databasebeta| order | 12794 |
| automorphism | Aut(G) order 40915212 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D6397 |
| unambiguous semidirect product | C6397⋊C2 |
| Fitting, socle, derived, Sylow | C6397 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6397 | C2 |
| LCS | G ▷ C6397 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,6397|b^a=b^63963200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #38784762, C2×D6397, D6397⋊C3, … |
| maximal normal subgroup of | #38784762, C2×D6397, D6397⋊C3, … |
| maximal quotient of | Dic6397, C2×D6397, C3×D6397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12794, 1);