Finite Group Databasebeta

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C3×C5×D3×C29⋊C7 #32912500

order18270
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D3×C29⋊C7
unambiguous semidirect productC3⋊(C2×C3×C5×C29⋊C7)
unambiguous semidirect product(D3×C29)⋊(C3×C5×C7)
unambiguous semidirect product(C3×D3×C29)⋊(C5×C7)
unambiguous semidirect product(C5×D3×C29)⋊(C3×C7)
unambiguous semidirect product(C3×C5×D3×C29)⋊C7

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C5D3×C29⋊C7
commutator, cosocle, hypocenterC3×C29C2×C3×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C29C2×C7
LCSG ▷ C3×C29
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 870

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C5×D3×D29⋊C7, C3×D3×C5⋊(D29⋊C7), C3×D3×D5×C29⋊C7, …
maximal normal subgroup ofC3×C5×D3×D29⋊C7, C3×D3×C5⋊(D29⋊C7), C3×D3×D5×C29⋊C7, …
maximal quotient ofC3×C5×Dic3×C29⋊C7, C2×C3×C5×D3×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 38);