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C2×C3×C5×D41⋊C5 #27134249

order12300
isoclinismisoclinic class of D41⋊C5
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C5×D41⋊C5
unambiguous semidirect productD41⋊(C2×C3×C52)
unambiguous semidirect product(C2×D41)⋊(C3×C52)
unambiguous semidirect product(C41⋊C5)⋊(C22×C3×C5)
unambiguous semidirect product(C2×C41⋊C5)⋊(C2×C3×C5)
unambiguous semidirect product(C2×C3×D41)⋊C52
unambiguous semidirect product(C2×C5×D41)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C5×D41)⋊C5

Splittings

Fitting, socleC2×C3×C5×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C22×C3×C52
HallC3×C5×C41⋊C5 ⋊ C22
HallC5×C41⋊C5 ⋊ C22×C3
HallC2×C3×D41 ⋊ C52
HallC2×D41 ⋊ C3×C52
HallC3×C41 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D41⋊C5
commutator, cosocle, hypocenterC41C22×C3×C52
FrattiniC1G
Fitting, socleC2×C3×C5×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C3×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C9×D41⋊C5, C3×C5×D3×D41⋊C5, C2×C32×C5×D41⋊C5, …
maximal normal subgroup ofC2×C5×C9×D41⋊C5, C2×C32×C5×D41⋊C5
maximal quotient ofC2×C5×C9×D41⋊C5, C3×C5×D3×D41⋊C5, C2×C32×C5×D41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 111);