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C5×C3⋊(D41⋊C5) #20259642

order6150
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C3⋊(D41⋊C5)
unambiguous semidirect productC3⋊(C5×D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(C5×D3)
unambiguous semidirect productD123⋊C52
unambiguous semidirect product(C5×D123)⋊C5

Splittings

Fitting, socleC3×C5×C41 ⋊ C2×C5
derived, HallC3×C41 ⋊ C2×C52
HallC3×C5×C41⋊C5 ⋊ C2
HallC5×C41⋊C5 ⋊ D3
HallD123 ⋊ C52
SylowC41 ⋊ C52×D3
SylowC3 ⋊ C5×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(D41⋊C5)
commutator, hypocenterC3×C41C2×C52
FrattiniC1G
Fitting, socleC3×C5×C41C2×C5
LCSG ▷ C3×C41
UCSC1 ◁ C5

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×D41⋊C5, D5×C3⋊(D41⋊C5), D15⋊(D41⋊C5), …
maximal normal subgroup ofC5×D3×D41⋊C5, D5×C3⋊(D41⋊C5), D15⋊(D41⋊C5), …
maximal quotient ofC5×C3⋊(Dic41⋊C5), C2×C5×C3⋊(D41⋊C5), C5×C9⋊(D41⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6150, 17);