Finite Group DatabasebetaFinite Group Databasebeta| order | 8164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C157 ⋊ C4 |
| Sylow | C157 ⋊ #261 |
| Sylow | C13 ⋊ #10597845 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C157 | C4 |
| LCS | G ▷ C13×C157 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,13,157|a^2=b,c^a=c^5,d^a=d^129,c^b=c^12,d^b=d^156514 conjugacy classes — view the full character table.
| maximal subgroup of | #37587597, #37587598, #37587602, … |
| maximal normal subgroup of | #37587597, #37587598, #37587602, … |
| maximal quotient of | C3×#22551027, C3⋊#22551027 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8164, 14);