Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C61 ⋊ C3×C4 |
| Hall | #15691761 ⋊ C3 |
| Hall | C13×C61⋊C3 ⋊ C4 |
| Hall | C61⋊C3 ⋊ Dic13 |
| Sylow | C61 ⋊ C3×Dic13 |
| Sylow | C13 ⋊ #6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C61 | C3×C4 |
| prime radical | C13×D61⋊C3 | C2 |
| cosocle | C13×D61 | C2×C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,13,61|a^2=c,d^a=d^12,e^a=e^50,e^b=e^13,e^c=e^60113 conjugacy classes — view the full character table.
| maximal subgroup of | #23748930⋊C3, C3×#23748943, C3⋊#23748943 |
| maximal normal subgroup of | #23748930⋊C3, C3×#23748943 |
| maximal quotient of | #43269666, C3×#23748943, C3⋊#23748943 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 52);