Finite Group DatabasebetaFinite Group Databasebeta| order | 4802 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C72 |
| direct product | C72×C7⋊D7 |
| unambiguous semidirect product | C7⋊(C72×D7) |
| Fitting, socle, Sylow | C74 ⋊ C2 |
| derived | C72 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C7⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C74 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C72 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 98 |
1274 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4802, 53);