Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C7⋊#6157 |
| unambiguous semidirect product | C7⋊(C7×#6157) |
| Fitting, socle, Hall | C72×C53 ⋊ C4 |
| derived | C7×C53 ⋊ C4×C7 |
| Sylow | C53 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ #6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊#6157 |
| commutator, hypocenter | C7×C53 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C53 | C4 |
| prime radical | C72×D53 | C2 |
| cosocle | C7×D53 | C2×C7 |
| LCS | G ▷ C7×C53 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
707 conjugacy classes — view the full character table.
| maximal subgroup of | #44528384, C7×ΓL(1,𝔽8)⋊#6157, ΓL(1,𝔽8)×C7⋊#6157, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)⋊#6157, ΓL(1,𝔽8)×C7⋊#6157, #44528409, … |
| maximal quotient of | C3×C7×C7⋊#6157, C7×C3⋊(C7⋊#6157) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 20);