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 | #261×C61 ⋊ C3 |
| Hall | #14558651 ⋊ C4 |
| Sylow | C61 ⋊ AGL(1,𝔽13) |
| Hall | #261 ⋊ C61⋊C3 |
| Sylow | C13 ⋊ C4×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C61 | C3×C4 |
| prime radical | #18011728 | C2 |
| cosocle | D13×C61 | 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^5,d^b=d^3,e^b=e^13,d^c=d^12153 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×C61⋊C3, C3×#23748927, C3⋊#23748927 |
| maximal normal subgroup of | AGL(1,𝔽13)×C61⋊C3, C3×#23748927 |
| maximal quotient of | #43269650, C3×#23748927, C3⋊#23748927 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 36);