Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊D101 |
| unambiguous semidirect product | D303⋊D7 |
| unambiguous semidirect product | D707⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C101 ⋊ C22 |
| Hall | C7×C101 ⋊ C2×D3 |
| Hall | C3×C101 ⋊ C2×D7 |
| Sylow | C101 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D101 |
| Sylow | C7 ⋊ D3×D101 |
| Sylow | C3 ⋊ D7×D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C101 | C22 |
| LCS | G ▷ C3×C7×C101 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,101|d^a=d^6,e^a=e^100,c^b=c^2,d^b=d^6615 conjugacy classes — view the full character table.
| maximal subgroup of | D63⋊D101, (C3⋊AGL(1,𝔽7))⋊D101, C3×D21⋊D101, … |
| maximal normal subgroup of | (C3⋊AGL(1,𝔽7))⋊D101, C3×D21⋊D101 |
| maximal quotient of | D63⋊D101, C3×D21⋊D101, D303⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 30);