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C5×C3⋊(C3⋊(D29⋊C7)) #32912503

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

Aliases

direct productC5×C3⋊(C3⋊(D29⋊C7))
unambiguous semidirect productC3⋊(C5×C3⋊(D29⋊C7))
unambiguous semidirect product(C29⋊C7)⋊(C5×C3⋊D3)
unambiguous semidirect product(C3⋊D87)⋊(C5×C7)
unambiguous semidirect product(C5×C3⋊D87)⋊C7

Splittings

Fitting, socle, HallC32×C5×C29 ⋊ C2×C7
derived, HallC32×C29 ⋊ C2×C5×C7
HallC32×C5×C29⋊C7 ⋊ C2
HallC5×C3⋊D87 ⋊ C7
HallC32×C29⋊C7 ⋊ C2×C5
HallC5×C29⋊C7 ⋊ C3⋊D3
HallC3⋊D87 ⋊ C5×C7
HallC29⋊C7 ⋊ C5×C3⋊D3
HallC5×C29 ⋊ C7×C3⋊D3
HallC32×C5 ⋊ D29⋊C7
SylowC29 ⋊ C5×C7×C3⋊D3
SylowC32 ⋊ C5×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊(D29⋊C7))
commutator, cosocle, hypocenterC32×C29C2×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C29C2×C7
LCSG ▷ C32×C29
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1305

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#11760329⋊C7, #19104889⋊C7, C5×D3×C3⋊(D29⋊C7), …
maximal normal subgroup ofC5×#11760329⋊C7, #19104889⋊C7, C5×D3×C3⋊(D29⋊C7), …
maximal quotient ofC5×C3⋊(C3⋊(Dic29⋊C7)), C2×C5×C3⋊(C3⋊(D29⋊C7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 41);