Finite Group Databasebeta

← Prev (#20264179) Next (#20264181) →

C2×C41×D13⋊C3 #20264180

order6396
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C41 · Schur multiplier (H2) = C2

Aliases

direct productC2×C41×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C41)
unambiguous semidirect product(C13⋊C3)⋊(C22×C41)
unambiguous semidirect product(C2×D13)⋊(C3×C41)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C41)
unambiguous semidirect product(C2×D13×C41)⋊C3

Splittings

Fitting, socleC2×C13×C41 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C41
HallC2×D13×C41 ⋊ C3
HallC13⋊C3×C41 ⋊ C22
HallC13×C41 ⋊ C22×C3
HallC2×D13 ⋊ C3×C41
HallC13⋊C3 ⋊ C22×C41

Subgroups

subgroupG/H
center, hypercenterC2×C41D13⋊C3
commutator, hypocenterC13C22×C3×C41
FrattiniC1G
Fitting, socleC2×C13×C41C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C41

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C41×D13⋊C3, C2×C3×C41×D13⋊C3, C2×C41×C3⋊(D13⋊C3), …
maximal normal subgroup ofC2×C3×C41×D13⋊C3, C2×D13⋊C3×C41⋊C5, C2×C5×C41×D13⋊C3
maximal quotient ofC2×C41×D13⋊C9, D3×C41×D13⋊C3, C2×C3×C41×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6396, 21);