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C7×C5⋊(D41⋊C5) #28385135

order14350
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊(D41⋊C5)
unambiguous semidirect productC5⋊(C7×D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(C7×D5)
unambiguous semidirect productD205⋊(C5×C7)
unambiguous semidirect product(C7×D205)⋊C5

Splittings

Fitting, socleC5×C7×C41 ⋊ C2×C5
derivedC5×C41 ⋊ C2×C5×C7
HallC5×C7×C41⋊C5 ⋊ C2
HallC5×C41⋊C5 ⋊ C2×C7
HallC7×C41 ⋊ C5×D5
SylowC41 ⋊ C5×C7×D5

Subgroups

subgroupG/H
center, hypercenterC7C5⋊(D41⋊C5)
commutator, cosocle, hypocenterC5×C41C2×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C41C2×C5
LCSG ▷ C5×C41
UCSC1 ◁ C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1435

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×#11717961⋊C5, C7×#11717962⋊C5, C7⋊(#11717961⋊C5), …
maximal normal subgroup ofC7×#11717961⋊C5, C7×#11717962⋊C5, C7⋊(#11717961⋊C5), …
maximal quotient ofC7×Dic205⋊C5, C2×C7×C5⋊(D41⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14350, 17);