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C2×C13⋊C3×C67⋊C3 #30627907

order15678
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC2×C13⋊C3×C67⋊C3
unambiguous semidirect product(C2×C13×C67⋊C3)⋊C3
unambiguous semidirect product(C2×C13⋊C3×C67)⋊C3
unambiguous semidirect product(C2×#14579732)⋊C3
unambiguous semidirect product(C2×#14579731)⋊C3

Splittings

Fitting, socle, HallC2×C13×C67 ⋊ C32
derived, HallC13×C67 ⋊ C2×C32
HallC2×C67 ⋊ C3×C13⋊C3
SylowC67 ⋊ C2×C3×C13⋊C3
HallC2×C13 ⋊ C3×C67⋊C3
SylowC13 ⋊ C2×C3×C67⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×C67⋊C3
commutator, cosocle, hypocenterC13×C67C2×C32
FrattiniC1G
Fitting, socleC2×C13×C67C32
LCSG ▷ C13×C67
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1742

Conjugacy classes & character table

350 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C67⋊C3)⋊(Dic13⋊C3), Dic13⋊C3×C67⋊C3, C13⋊C3×(C67⋊C3)⋊C4, …
maximal normal subgroup of(C67⋊C3)⋊(Dic13⋊C3), Dic13⋊C3×C67⋊C3, C13⋊C3×(C67⋊C3)⋊C4, …
maximal quotient ofC4×C13⋊C3×C67⋊C3, C22×C13⋊C3×C67⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15678, 29);