Finite Group DatabasebetaFinite Group Databasebeta| order | 4996 |
| automorphism | Aut(G) order 3117504 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1249 |
| derived, Sylow | C1249 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1249 |
| commutator, hypocenter | C1249 | C4 |
| Fitting, socle | C2×C1249 | C2 |
| LCS | G ▷ C1249 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1249|a^2=b,c^a=c^12481252 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic1249⋊C3, C3×Dic1249, Dic3747, … |
| maximal normal subgroup of | Dic1249⋊C3, C3×Dic1249, C5×Dic1249, … |
| maximal quotient of | C3×Dic1249, Dic3747, C5×Dic1249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4996, 1);