Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C61 ⋊ C3×C4 |
| Hall | Dic13×C61 ⋊ C3 |
| Hall | #14558651 ⋊ C4 |
| Sylow | C61 ⋊ Dic13⋊C3 |
| Hall | Dic13 ⋊ C61⋊C3 |
| Sylow | C13 ⋊ C4×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #18011728 |
| commutator, hypocenter | C13×C61 | C3×C4 |
| Fitting, socle, cosocle | C2×C13×C61 | C2×C3 |
| prime radical | C2×#14558651 | C2 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,61,2|a^2=e,c^a=c^12,c^b=c^3,d^b=d^13336 conjugacy classes — view the full character table.
| maximal subgroup of | Dic13⋊C3×C61⋊C3, C3×#23748911, C3⋊#23748911 |
| maximal normal subgroup of | Dic13⋊C3×C61⋊C3, C3×#23748911 |
| maximal quotient of | #43269634, C3×#23748911, C3⋊#23748911 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 20);