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C5×D3×C41⋊C5 #20259643

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

Aliases

direct productC5×D3×C41⋊C5
unambiguous semidirect productC3⋊(C2×C5×C41⋊C5)
unambiguous semidirect product(D3×C41)⋊C52
unambiguous semidirect product(C5×D3×C41)⋊C5

Splittings

Fitting, socleC3×C5×C41 ⋊ C2×C5
derived, HallC3×C41 ⋊ C2×C52
HallC3×C5×C41⋊C5 ⋊ C2
HallD3×C41 ⋊ C52
SylowC41 ⋊ C52×D3
SylowC3 ⋊ C2×C5×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC5D3×C41⋊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

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×D41⋊C5, D3×C5⋊(D41⋊C5), D3×D5×C41⋊C5, …
maximal normal subgroup ofC5×D3×D41⋊C5, D3×C5⋊(D41⋊C5), D3×D5×C41⋊C5, …
maximal quotient ofC5×Dic3×C41⋊C5, C2×C5×D3×C41⋊C5, C5×D9×C41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6150, 18);