Finite Group Databasebeta

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C72×C3⋊(D19⋊C3) #30660802

order16758
isoclinismisoclinic class of C3⋊(D19⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×C3⋊(D19⋊C3)
unambiguous semidirect productC3⋊(C72×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(D3×C72)
unambiguous semidirect productD57⋊(C3×C72)

Splittings

Fitting, socleC3×C72×C19 ⋊ C2×C3
derivedC3×C19 ⋊ C2×C3×C72
HallC3×C72×C19⋊C3 ⋊ C2
HallC72×C19 ⋊ C3×D3
HallC3×C19⋊C3 ⋊ C2×C72
SylowC19 ⋊ C3×D3×C72

Subgroups

subgroupG/H
center, hypercenterC72C3⋊(D19⋊C3)
commutator, cosocle, hypocenterC3×C19C2×C3×C72
FrattiniC1G
Fitting, socleC3×C72×C19C2×C3
LCSG ▷ C3×C19
UCSC1 ◁ C72

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2793

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C72×D19⋊C3, C7×D7×C3⋊(D19⋊C3), C7×(C3⋊(D19⋊C3))⋊D7, …
maximal normal subgroup ofD3×C72×D19⋊C3, C7×D7×C3⋊(D19⋊C3), C7×(C3⋊(D19⋊C3))⋊D7, …
maximal quotient ofC72×C3⋊((C19⋊C3)⋊C4), C2×C72×C3⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 329);