Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊(C7⋊#6157) |
| Fitting, socle, derived, Hall | C72×C53 ⋊ C4 |
| Sylow | C53 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ #6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C53 | C4 |
| prime radical, cosocle | C72×D53 | C2 |
| LCS | G ▷ C72×C53 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7^2,53|a^2=b,c^a=c^6,d^a=d^6,e^a=e^30,e^b=e^52689 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊(C7⋊#6157), #44528407, #44528420, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊(C7⋊#6157), #44528407, #44528420, … |
| maximal quotient of | C3×C7⋊(C7⋊#6157), C3⋊(C7⋊(C7⋊#6157)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 22);