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C3×(C13⋊C3)⋊D43 #23758472

order10062
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C13⋊C3)⋊D43
unambiguous semidirect product(C13⋊C3)⋊(C3×D43)

Splittings

Fitting, socleC3×C13×C43 ⋊ C2×C3
derived, HallC13×C43 ⋊ C2×C32
HallC3×C13⋊C3×C43 ⋊ C2
HallD559 ⋊ C32
HallC3×C13⋊C3 ⋊ D43
SylowC43 ⋊ C3×D13⋊C3
SylowC13 ⋊ C32×D43

Subgroups

subgroupG/H
center, hypercenterC3(C13⋊C3)⋊D43
commutator, cosocle, hypocenterC13×C43C2×C32
FrattiniC1G
Fitting, socleC3×C13×C43C2×C3
LCSG ▷ C13×C43
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

465 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D13⋊C3×D43, D3×(C13⋊C3)⋊D43, (C3⋊(D13⋊C3))⋊D43, …
maximal normal subgroup ofC3×D13⋊C3×D43, D3×(C13⋊C3)⋊D43, (C3⋊(D13⋊C3))⋊D43, …
maximal quotient ofC3×#20269442, C2×C3×(C13⋊C3)⋊D43

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10062, 36);