Finite Group DatabasebetaFinite Group Databasebeta| order | 7300 |
| automorphism | Aut(G) order 5256000 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1825 |
| derived, Hall | C25×C73 ⋊ C4 |
| Sylow | C73 ⋊ Dic25 |
| Sylow | C25 ⋊ Dic73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1825 |
| commutator, hypocenter | C25×C73 | C4 |
| Frattini | C2×C5 | D365 |
| Fitting | C2×C25×C73 | C2 |
| socle | C2×C5×C73 | D5 |
| LCS | G ▷ C25×C73 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,73,2,5|a^2=d,b^5=e^4,b^a=b^4e,c^a=c^72,e^a=e^41828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1825, Dic5475, Dic1825⋊C3, … |
| maximal normal subgroup of | C3×Dic1825, Dic1825⋊C3, Dic3650 |
| maximal quotient of | C3×Dic1825, Dic5475, Dic9125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7300, 4);