Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | Aut(G) order 6851520 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2379 |
| unambiguous semidirect product | C3⋊Dic793 |
| derived, Hall | C3×C13×C61 ⋊ C4 |
| Hall | C13×C61 ⋊ Dic3 |
| Hall | C3×C61 ⋊ Dic13 |
| Sylow | C61 ⋊ Dic39 |
| Hall | C3×C13 ⋊ Dic61 |
| Sylow | C13 ⋊ Dic183 |
| Sylow | C3 ⋊ Dic793 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2379 |
| commutator, hypocenter | C3×C13×C61 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C13×C61 | C2 |
| LCS | G ▷ C3×C13×C61 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,61,2|a^2=e,b^a=b^2,c^a=c^12,d^a=d^602382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7137, C3⋊#23748915, C3⋊#23748914, … |
| maximal normal subgroup of | C3⋊#23748915, C3⋊#23748914, C3⋊#23748913, … |
| maximal quotient of | Dic7137, C3⋊Dic2379, C3×Dic2379 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 12);