Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | D39×C7⋊D7 |
| Fitting, socle, derived, Hall | C3×C72×C13 ⋊ C22 |
| Hall | C72×C13 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D13 |
| Sylow | C72 ⋊ C2×D39 |
| Hall | C3×C13 ⋊ C2×C7⋊D7 |
| Sylow | C13 ⋊ D3×C7⋊D7 |
| Sylow | C3 ⋊ D13×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C13 | C22 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
546 conjugacy classes — view the full character table.
| maximal subgroup of | C7⋊D7×D117, #37525186, #37525187, … |
| maximal normal subgroup of | #37525186, #37525187, D39×ΓL(1,𝔽8)⋊D7, … |
| maximal quotient of | C7⋊D7×D117, C3×D39×C7⋊D7, D39×C3⋊(C7⋊D7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 335);