Finite Group DatabasebetaFinite Group Databasebeta| order | 12898 |
| automorphism | Aut(G) order 41583152 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D6449 |
| unambiguous semidirect product | C6449⋊C2 |
| Fitting, socle, derived, Sylow | C6449 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6449 | C2 |
| LCS | G ▷ C6449 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,6449|b^a=b^64483226 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #38788703, C2×D6449 |
| maximal normal subgroup of | #38788703, C2×D6449 |
| maximal quotient of | Dic6449, C2×D6449 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12898, 1);