Finite Group Databasebeta

← Prev (#20264180) Next (#20264182) →

C2×(C13⋊C3)⋊D41 #20264181

order6396
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C13⋊C3)⋊D41
unambiguous semidirect product(C2×C13⋊C3)⋊D41
unambiguous semidirect product(C2×C41)⋊(D13⋊C3)
unambiguous semidirect product(C2×D533)⋊C3

Splittings

Fitting, socleC2×C13×C41 ⋊ C2×C3
derived, HallC13×C41 ⋊ C22×C3
HallC2×D533 ⋊ C3
HallC13⋊C3×C41 ⋊ C22
SylowC41 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×D41
SylowC13 ⋊ C2×C3×D41

Subgroups

subgroupG/H
center, hypercenterC2(C13⋊C3)⋊D41
commutator, hypocenterC13×C41C22×C3
FrattiniC1G
Fitting, socleC2×C13×C41C2×C3
LCSG ▷ C13×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

296 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×(C13⋊C3)⋊D41, C2×C3×(C13⋊C3)⋊D41, C2×C3⋊((C13⋊C3)⋊D41), …
maximal normal subgroup ofC2×C3×(C13⋊C3)⋊D41, C2×(C13⋊C3)⋊(D41⋊C5), C2×C5×(C13⋊C3)⋊D41
maximal quotient ofC2×C41⋊(D13⋊C9), D3×(C13⋊C3)⋊D41, C2×C3×(C13⋊C3)⋊D41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6396, 22);