Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D371 |
| unambiguous semidirect product | (C7×D7)⋊D53 |
| unambiguous semidirect product | (D7×C53)⋊D7 |
| Fitting, socle, derived, Hall | C72×C53 ⋊ C22 |
| Sylow | C53 ⋊ D72 |
| Sylow | C72 ⋊ C2×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C53 | C22 |
| LCS | G ▷ C72×C53 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
935 conjugacy classes — view the full character table.
| maximal subgroup of | #64418⋊D53, D7×ΓL(1,𝔽8)⋊D53, AGL(1,𝔽7)×D371, … |
| maximal normal subgroup of | D7×ΓL(1,𝔽8)⋊D53, AGL(1,𝔽7)×D371, #64423⋊D53, … |
| maximal quotient of | C3×D7×D371, D7×D1113, D21×D371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 25);