Finite Group DatabasebetaFinite Group Databasebeta| order | 6994 |
| automorphism | Aut(G) order 11246352 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3497 |
| unambiguous semidirect product | C13⋊D269 |
| unambiguous semidirect product | C269⋊D13 |
| Fitting, socle, derived, Hall | C13×C269 ⋊ C2 |
| Sylow | C269 ⋊ D13 |
| Sylow | C13 ⋊ D269 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C269 | C2 |
| LCS | G ▷ C13×C269 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,269|b^a=b^12,c^a=c^2681750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28380196, #28380197, D13×D269, … |
| maximal normal subgroup of | #28380196, #28380197, D13×D269, … |
| maximal quotient of | Dic3497, C2×D3497, C3×D3497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6994, 3);