Finite Group DatabasebetaFinite Group Databasebeta| order | 8364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#14584033 |
| Fitting, socle, derived, Hall | C3×C17×C41 ⋊ C4 |
| Hall | C17×C41 ⋊ Dic3 |
| Hall | C3×C41 ⋊ #595 |
| Hall | C3×C17 ⋊ #4223 |
| Sylow | C41 ⋊ C3⋊#595 |
| Sylow | C17 ⋊ C3⋊#4223 |
| Sylow | C3 ⋊ #14584033 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C41 | C4 |
| LCS | G ▷ C3×C17×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17,41|a^2=b,c^a=c^2,d^a=d^13,e^a=e^9,d^b=d^16,e^b=e^40528 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#14584033, C3×C3⋊#14584033, C3⋊(C3⋊#14584033) |
| maximal normal subgroup of | C3×C3⋊#14584033 |
| maximal quotient of | C9⋊#14584033, C3×C3⋊#14584033, C3⋊(C3⋊#14584033) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8364, 21);