Finite Group Databasebeta

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C3×D15×C43⋊C7 #41029142

order27090
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×D15×C43⋊C7
unambiguous semidirect productC3⋊(C3×D5×C43⋊C7)
unambiguous semidirect productC5⋊(C3×D3×C43⋊C7)
unambiguous semidirect product(C3×D15×C43)⋊C7

Splittings

Fitting, socle, HallC32×C5×C43 ⋊ C2×C7
derivedC3×C5×C43 ⋊ C2×C3×C7
HallC32×C5×C43⋊C7 ⋊ C2
HallC3×D15×C43 ⋊ C7
HallC32×C43⋊C7 ⋊ D5
HallC5×C43⋊C7 ⋊ C3×D3
HallC32×C43 ⋊ C7×D5
HallC5×C43 ⋊ C3×D3×C7
HallC32×C5 ⋊ C2×C43⋊C7
SylowC43 ⋊ C3×C7×D15
SylowC32 ⋊ D5×C43⋊C7
SylowC5 ⋊ C3×D3×C43⋊C7

Subgroups

subgroupG/H
center, hypercenterC3D15×C43⋊C7
commutator, cosocle, hypocenterC3×C5×C43C2×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C43C2×C7
LCSG ▷ C3×C5×C43
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1290

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27090, 83);