Finite Group DatabasebetaFinite Group Databasebeta| order | 6700 |
| automorphism | Aut(G) order 4422000 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1675 |
| unambiguous semidirect product | C67⋊Dic25 |
| derived, Hall | C25×C67 ⋊ C4 |
| Sylow | C67 ⋊ Dic25 |
| Sylow | C25 ⋊ Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1675 |
| commutator, hypocenter | C25×C67 | C4 |
| Frattini | C2×C5 | D335 |
| Fitting | C2×C25×C67 | C2 |
| socle | C2×C5×C67 | D5 |
| LCS | G ▷ C25×C67 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,67,2,5|a^2=d,b^5=e^4,b^a=b^4e,c^a=c^66,e^a=e^41678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1675, Dic5025, (C67⋊C3)⋊Dic25, … |
| maximal normal subgroup of | C3×Dic1675, (C67⋊C3)⋊Dic25, Dic3350 |
| maximal quotient of | C3×Dic1675, Dic5025, Dic8375 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6700, 4);