Finite Group DatabasebetaFinite Group Databasebeta| order | 3318 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C79 ⋊ C2×C3 |
| Hall | #13110306 ⋊ C2 |
| Hall | D7×C79 ⋊ C3 |
| Sylow | C79 ⋊ AGL(1,𝔽7) |
| Hall | D7 ⋊ C79⋊C3 |
| Sylow | C7 ⋊ C2×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C79 | C2×C3 |
| LCS | G ▷ C7×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 86 |
| transitive degree | μt(G) = 553 |
Polycyclic presentation:
2,3,7,79|c^a=c^6,c^b=c^2,d^b=d^55137 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#15693303, C5⋊#15693303, #37551101, … |
| maximal normal subgroup of | C5×#15693303, C7×#15693303, C11×#15693303 |
| maximal quotient of | C5×#15693303, C5⋊#15693303, #37551101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3318, 20);