Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C7 |
| direct product | C43×C7⋊Dic7 |
| unambiguous semidirect product | C7⋊(Dic7×C43) |
| derived, Sylow | C72 ⋊ C4×C43 |
| Hall | C72×C43 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | C7⋊D7 |
| commutator, hypocenter | C72 | C4×C43 |
| Frattini | C2 | C43×C7⋊D7 |
| Fitting, socle | C2×C72×C43 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C43 | |
60 conjugacy classes of subgroups.
2236 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#10596874, #38760313, #38760314, … |
| maximal normal subgroup of | C43×#10596874, #38760313, #38760314, … |
| maximal quotient of | C43×C3⋊(C7⋊Dic7), C3×C43×C7⋊Dic7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 22);