Finite Group DatabasebetaFinite Group Databasebeta| order | 10380 |
| automorphism | Aut(G) order 7141440 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2595 |
| unambiguous semidirect product | C3⋊Dic865 |
| derived, Hall | C3×C5×C173 ⋊ C4 |
| Hall | C5×C173 ⋊ Dic3 |
| Hall | C3×C173 ⋊ Dic5 |
| Sylow | C173 ⋊ Dic15 |
| Hall | C3×C5 ⋊ Dic173 |
| Sylow | C5 ⋊ Dic519 |
| Sylow | C3 ⋊ Dic865 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2595 |
| commutator, hypocenter | C3×C5×C173 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C173 | C2 |
| LCS | G ▷ C3×C5×C173 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,173,2|a^2=e,b^a=b^2,c^a=c^4,d^a=d^1722598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7785, C3⋊Dic2595, C3×Dic2595, … |
| maximal normal subgroup of | C3×Dic2595, Dic5190 |
| maximal quotient of | Dic7785, C3⋊Dic2595, C3×Dic2595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10380, 8);