Finite Group Databasebeta

← Prev (#22547421) Next (#22547423) →

C2×C3×C17×D13⋊C3 #22547422

order7956
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C17×D13⋊C3
unambiguous semidirect productD13⋊(C2×C32×C17)
unambiguous semidirect product(C13⋊C3)⋊(C22×C3×C17)
unambiguous semidirect product(C2×D13)⋊(C32×C17)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C3×C17)
unambiguous semidirect product(C2×C3×D13)⋊(C3×C17)
unambiguous semidirect product(C2×C17×D13)⋊C32
unambiguous semidirect product(C2×C3×C17×D13)⋊C3

Splittings

Fitting, socleC2×C3×C13×C17 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C32×C17
HallC3×C17×C13⋊C3 ⋊ C22
HallC2×C17×D13 ⋊ C32
HallC13×C17 ⋊ C22×C32
HallC3×C13⋊C3 ⋊ C22×C17
HallC2×D13 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D13⋊C3
commutator, hypocenterC13C22×C32×C17
FrattiniC1G
Fitting, socleC2×C3×C13×C17C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C17

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

816 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7956, 94);