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C11⋊C5×D147 #30633480

order16170
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D147
unambiguous semidirect productC3⋊(C11⋊C5×D49)
unambiguous semidirect productC49⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D147)⋊C5

Splittings

Fitting, derived, HallC3×C11×C49 ⋊ C2×C5
HallC3×C49×C11⋊C5 ⋊ C2
HallC11×D147 ⋊ C5
HallC49×C11⋊C5 ⋊ D3
HallC11×C49 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ D49
HallC3×C49 ⋊ C2×C11⋊C5
SylowC49 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C5×D49
SylowC11 ⋊ C5×D147
SylowC3 ⋊ C11⋊C5×D49

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C11×C49C2×C5
FrattiniC7D21×C11⋊C5
socleC3×C7×C11C5×D7
LCSG ▷ C3×C11×C49
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

525 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D147, D147⋊AGL(1,𝔽11), D3×C11⋊C5×D49, …
maximal normal subgroup ofAGL(1,𝔽11)×D147, D147⋊AGL(1,𝔽11), D3×C11⋊C5×D49, …
maximal quotient ofC11⋊C5×Dic147, C2×C11⋊C5×D147

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 25);