Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C7×C101 ⋊ C22×C3 |
| Hall | D7×D101 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C101 ⋊ C22 |
| Sylow | C101 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C2×D101 |
| Sylow | C7 ⋊ C2×C3×D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C101 | C22×C3 |
| LCS | G ▷ C7×C101 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽7)×D101, C3⋊AGL(1,𝔽7)×D101, AGL(1,𝔽7)×D303, … |
| maximal normal subgroup of | C3×AGL(1,𝔽7)×D101 |
| maximal quotient of | D7⋊C9×D101, C3×AGL(1,𝔽7)×D101, C3⋊AGL(1,𝔽7)×D101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 15);