Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic371 |
| derived, Hall | C72×C53 ⋊ C4 |
| Sylow | C53 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊D371 |
| commutator, hypocenter | C72×C53 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C72×C53 | C2 |
| LCS | G ▷ C72×C53 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,7^2,53,2|a^2=e,b^a=b^6,c^a=c^6,d^a=d^522600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44528354, #44528356, ΓL(1,𝔽8)⋊Dic371, … |
| maximal normal subgroup of | #44528354, #44528356, ΓL(1,𝔽8)⋊Dic371, … |
| maximal quotient of | C3⋊(C7⋊Dic371), C3×C7⋊Dic371 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 17);