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C3×D5×C41⋊C5 #20259641

order6150
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C41⋊C5
unambiguous semidirect productC5⋊(C2×C3×C41⋊C5)
unambiguous semidirect product(D5×C41)⋊(C3×C5)
unambiguous semidirect product(C3×D5×C41)⋊C5

Splittings

Fitting, socleC3×C5×C41 ⋊ C2×C5
derivedC5×C41 ⋊ C2×C3×C5
HallC3×C5×C41⋊C5 ⋊ C2
HallC5×C41⋊C5 ⋊ C2×C3
HallC3×C41 ⋊ C5×D5
SylowC41 ⋊ C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC3D5×C41⋊C5
commutator, hypocenterC5×C41C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C41C2×C5
LCSG ▷ C5×C41
UCSC1 ◁ C3

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#11717963⋊C5, C3×AGL(1,𝔽5)×C41⋊C5, C3×D5×D41⋊C5, …
maximal normal subgroup ofC3×#11717963⋊C5, C3×AGL(1,𝔽5)×C41⋊C5, C3×D5×D41⋊C5, …
maximal quotient ofC3×Dic5×C41⋊C5, C2×C3×D5×C41⋊C5, C9×D5×C41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6150, 16);