Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×#6157 |
| Fitting, socle, Hall | C72×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C4×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | #6157 |
| commutator, hypocenter | C53 | C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C53 | C4 |
| prime radical | C72×D53 | C2 |
| cosocle | D53 | C2×C72 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C72 | |
60 conjugacy classes of subgroups.
833 conjugacy classes — view the full character table.
| maximal subgroup of | C7×ΓL(1,𝔽8)×#6157, #3861×#6157, #3862×#6157, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)×#6157, #3861×#6157, #3862×#6157, … |
| maximal quotient of | C3×C72×#6157, C72×C3⋊#6157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 19);