Finite Group Databasebeta

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C2×C7×D361⋊C3 #44476447

order30324
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D361⋊C3
unambiguous semidirect productD361⋊(C2×C3×C7)
unambiguous semidirect product(C361⋊C3)⋊(C22×C7)
unambiguous semidirect product(C2×D361)⋊(C3×C7)
unambiguous semidirect product(C2×C361⋊C3)⋊(C2×C7)

Splittings

FittingC2×C7×C361 ⋊ C2×C3
derived, SylowC361 ⋊ C22×C3×C7
HallC2×C7×D361 ⋊ C3
HallC7×C361⋊C3 ⋊ C22
HallC7×C361 ⋊ C22×C3
HallC2×D361 ⋊ C3×C7
HallC361⋊C3 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D361⋊C3
commutator, cosocle, hypocenterC361C22×C3×C7
FrattiniC19C2×C7×D19⋊C3
FittingC2×C7×C361C2×C3
socleC2×C7×C19D19⋊C3
LCSG ▷ C361
UCSC1 ◁ C2×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5054

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30324, 30);