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C3×C5×C3⋊(C7⋊D7) #17984406

order4410
isoclinismisoclinic class of C3⋊(C7⋊D7)
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×C3⋊(C7⋊D7)
unambiguous semidirect productC3⋊(C3×C5×C7⋊D7)

Splittings

Fitting, socle, HallC32×C5×C72 ⋊ C2
derivedC3×C72 ⋊ C2×C3×C5
HallC32×C72 ⋊ C2×C5
HallC5×C72 ⋊ C3×D3
SylowC72 ⋊ C3×C5×D3
HallC32×C5 ⋊ C7⋊D7
SylowC32 ⋊ C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C72C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C72C2
LCSG ▷ C3×C72
UCSC1 ◁ C3×C5

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1470

Conjugacy classes & character table

1125 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C25×C3⋊(C7⋊D7), C3×C52×C3⋊(C7⋊D7), C3×C5×C3⋊(C5⋊(C7⋊D7))
maximal normal subgroup ofC3×C25×C3⋊(C7⋊D7), C3×C52×C3⋊(C7⋊D7)
maximal quotient ofC3×C25×C3⋊(C7⋊D7), C3×C52×C3⋊(C7⋊D7), C3×C5×C3⋊(C5⋊(C7⋊D7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4410, 127);