Finite Group DatabasebetaFinite Group Databasebeta| order | 4802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#10621859 |
| Fitting, Sylow | C7×H(3,𝔽7) ⋊ C2 |
| derived | H(3,𝔽7) ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C72 | C7⋊D7 |
| commutator, cosocle, hypocenter | H(3,𝔽7) | C2×C7 |
| Frattini | C7 | C7×C7⋊D7 |
| Fitting | C7×H(3,𝔽7) | C2 |
| LCS | G ▷ H(3,𝔽7) | |
| UCS | C1 ◁ C72 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 343 |
266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4802, 46);