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C3×C7×D41⋊C5 #22575563

order8610
isoclinismisoclinic class of D41⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D41⋊C5
unambiguous semidirect productD41⋊(C3×C5×C7)
unambiguous semidirect product(C41⋊C5)⋊(C2×C3×C7)
unambiguous semidirect product(C3×D41)⋊(C5×C7)
unambiguous semidirect product(C3×C7×D41)⋊C5

Splittings

Fitting, socle, HallC3×C7×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C2×C3×C5×C7
HallC3×C7×C41⋊C5 ⋊ C2
HallC3×C7×D41 ⋊ C5
HallC7×C41⋊C5 ⋊ C2×C3
HallC3×C41⋊C5 ⋊ C2×C7
HallC7×D41 ⋊ C3×C5
HallC7×C41 ⋊ C2×C3×C5
HallC3×D41 ⋊ C5×C7
HallC41⋊C5 ⋊ C2×C3×C7
HallC3×C41 ⋊ C2×C5×C7
HallD41 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C7D41⋊C5
commutator, hypocenterC41C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

294 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C7×#4223⋊C5, C3×C7⋊(#4223⋊C5), C3×D7×D41⋊C5, …
maximal normal subgroup ofC3×C7×#4223⋊C5, C3×C7⋊(#4223⋊C5), C3×D7×D41⋊C5, …
maximal quotient ofC3×C7×Dic41⋊C5, C2×C3×C7×D41⋊C5, C7×C9×D41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8610, 20);