Finite Group DatabasebetaFinite Group Databasebeta| order | 4802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, Sylow | #14558879 ⋊ C2 |
| derived | C7×C49 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C49 | C2×C7 |
| Frattini | C72 | C7×D7 |
| Fitting | #14558879 | C2 |
| socle | C7 | (C7⋊D7)⋊C7 |
| LCS | G ▷ C7×C49 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 343 |
| transitive degree | μt(G) = 343 |
Polycyclic presentation:
2,7^4|c^7=e^3,c^a=c^6e^4,d^a=d^6,e^a=e^6,c^b=cd,d^b=de59 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4802, 34);