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C3×(C271⋊C3)⋊C5 #27131900

order12195
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C271⋊C3)⋊C5
unambiguous semidirect product(C271⋊C3)⋊(C3×C5)
unambiguous semidirect product(C271⋊C5)⋊C32
unambiguous semidirect product(C3×C271⋊C3)⋊C5
unambiguous semidirect product(C3×C271⋊C5)⋊C3

Splittings

Fitting, socleC3×C271 ⋊ C3×C5
derived, SylowC271 ⋊ C32×C5
HallC3×C271⋊C3 ⋊ C5
HallC271⋊C5 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3(C271⋊C3)⋊C5
commutator, cosocle, hypocenterC271C32×C5
FrattiniC1G
Fitting, socleC3×C271C3×C5
LCSG ▷ C271
UCSC1 ◁ C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(D271⋊C3)⋊C5, C3⋊((D271⋊C3)⋊C5), D3×(C271⋊C3)⋊C5, …
maximal normal subgroup ofC3×(D271⋊C3)⋊C5, C3⋊((D271⋊C3)⋊C5), D3×(C271⋊C3)⋊C5, …
maximal quotient ofC2×C3×(C271⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12195, 7);