Finite Group DatabasebetaFinite Group Databasebeta| order | 2044 |
| isoclinism | isoclinic class of C7⋊#64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#64408 |
| Fitting, socle, derived, Hall | C7×C73 ⋊ C4 |
| Sylow | C73 ⋊ Dic7 |
| Sylow | C7 ⋊ #64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C73 | C4 |
| prime radical, cosocle | C7×D73 | C2 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 511 |
Polycyclic presentation:
2^2,7,73|a^2=b,c^a=c^6,d^a=d^27,d^b=d^72136 conjugacy classes — view the full character table.
| maximal subgroup of | C49⋊#64408, C7×C7⋊#64408, C7⋊(C7⋊#64408), … |
| maximal normal subgroup of | C7×C7⋊#64408, C11×C7⋊#64408, C13×C7⋊#64408, … |
| maximal quotient of | C49⋊#64408, C7×C7⋊#64408, C7⋊(C7⋊#64408), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2044, 7);