Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D7×#10587716 |
| Fitting, socle, derived, Hall | C72×C13 ⋊ C22×C3 |
| Hall | C7×D7×D13 ⋊ C3 |
| Hall | C7×#63270 ⋊ C22 |
| Sylow | C72 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ C2×D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C13 | C22×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
120 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#10587716, #37524899, #37524901, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#10587716, #37524899, #37524901, … |
| maximal quotient of | D7×#13109896, C3×D7×#10587716, D21×#10587716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 229);