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C2×C13⋊C3×D41 #20264182

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

Aliases

direct productC2×C13⋊C3×D41
unambiguous semidirect productC41⋊(C22×C13⋊C3)
unambiguous semidirect product(C2×C41)⋊(C2×C13⋊C3)
unambiguous semidirect product(C2×C13×D41)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2C13⋊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

308 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C13⋊C3×D41, C2×C3×C13⋊C3×D41, C2×C13⋊C3×D123, …
maximal normal subgroup ofC2×C3×C13⋊C3×D41, C2×C13⋊C3×D41⋊C5, C2×C5×C13⋊C3×D41
maximal quotient ofC2×D41×C13⋊C9, D3×C13⋊C3×D41, C2×C3×C13⋊C3×D41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6396, 23);