Finite Group DatabasebetaFinite Group Databasebeta| order | 4802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C76 |
| unambiguous semidirect product | C7⋊(C7⋊(C7⋊D7)) |
| Fitting, socle, derived, Sylow | C74 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C74 | C2 |
| LCS | G ▷ C74 | |
| UCS | C1 | |
7304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2401 |
Polycyclic presentation:
2,7^4|b^a=b^6,c^a=c^6,d^a=d^6,e^a=e^61202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4802, 54);