Finite Group DatabasebetaFinite Group Databasebeta| order | 6988 |
| automorphism | Aut(G) order 6100524 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1747 |
| unambiguous semidirect product | C1747⋊C4 |
| derived, Sylow | C1747 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1747 |
| commutator, hypocenter | C1747 | C4 |
| Fitting, socle | C2×C1747 | C2 |
| LCS | G ▷ C1747 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1747|a^2=b,c^a=c^17461750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1747, C2×Dic1747, C22⋊D1747, … |
| maximal normal subgroup of | C4×D1747, C2×Dic1747, C22⋊D1747, … |
| maximal quotient of | C1747⋊C8, C2×Dic1747, C3×Dic1747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6988, 1);