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C3×D15×C29⋊C7 #32912502

order18270
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×D15×C29⋊C7
unambiguous semidirect productC3⋊(C3×D5×C29⋊C7)
unambiguous semidirect productC5⋊(C3×D3×C29⋊C7)
unambiguous semidirect product(C29×D15)⋊(C3×C7)
unambiguous semidirect product(C3×C29×D15)⋊C7

Splittings

Fitting, socle, HallC32×C5×C29 ⋊ C2×C7
derivedC3×C5×C29 ⋊ C2×C3×C7
HallC32×C5×C29⋊C7 ⋊ C2
HallC3×C29×D15 ⋊ C7
HallC32×C29⋊C7 ⋊ D5
HallC5×C29⋊C7 ⋊ C3×D3
HallC32×C29 ⋊ C7×D5
HallC5×C29 ⋊ C3×D3×C7
HallC32×C5 ⋊ C2×C29⋊C7
SylowC29 ⋊ C3×C7×D15
SylowC32 ⋊ D5×C29⋊C7
SylowC5 ⋊ C3×D3×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC3D15×C29⋊C7
commutator, cosocle, hypocenterC3×C5×C29C2×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C29C2×C7
LCSG ▷ C3×C5×C29
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 870

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D15×D29⋊C7, C3×D15⋊(D29⋊C7), C3×D3×D5×C29⋊C7, …
maximal normal subgroup ofC3×D15×D29⋊C7, C3×D15⋊(D29⋊C7), C3×D3×D5×C29⋊C7, …
maximal quotient ofC3×Dic15×C29⋊C7, C2×C3×D15×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 40);