Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C7 |
| direct product | C53×C7⋊Dic7 |
| unambiguous semidirect product | C7⋊(Dic7×C53) |
| derived, Sylow | C72 ⋊ C4×C53 |
| Hall | C72×C53 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | C7⋊D7 |
| commutator, hypocenter | C72 | C4×C53 |
| Frattini | C2 | C53×C7⋊D7 |
| Fitting, socle, prime radical | C2×C72×C53 | C2 |
| cosocle | C2×C72 | C2×C53 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C53 | |
60 conjugacy classes of subgroups.
2756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#10596874, C53×#10596875, C53×ΓL(1,𝔽8)⋊Dic7, … |
| maximal normal subgroup of | C53×#10596874, C53×#10596875, C53×ΓL(1,𝔽8)⋊Dic7, … |
| maximal quotient of | C53×C3⋊(C7⋊Dic7), C3×C53×C7⋊Dic7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 16);