Finite Group DatabasebetaFinite Group Databasebeta| order | 3822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C13 ⋊ C2×C3 |
| Hall | C7×#63270 ⋊ C2 |
| Hall | C7⋊D91 ⋊ C3 |
| Sylow | C72 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C13 | C2×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 273 |
Polycyclic presentation:
2,3,7^2,13|c^a=c^6,d^a=d^6,e^a=e^12,c^b=c^2,e^b=e^3120 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊#10587722, #26039517, #26039518, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#10587722, #26039517, #26039518, … |
| maximal quotient of | #26039466, C3×#16838468, C3⋊#16838468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3822, 61);