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C11⋊C5×D51 #19150511

order5610
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D51
unambiguous semidirect productC3⋊(D17×C11⋊C5)
unambiguous semidirect productC17⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D51)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C17 ⋊ C2×C5
HallC3×C17×C11⋊C5 ⋊ C2
HallC11×D51 ⋊ C5
HallC17×C11⋊C5 ⋊ D3
HallC11×C17 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ D17
HallC3×C17 ⋊ C2×C11⋊C5
HallC3×C11 ⋊ C5×D17
SylowC17 ⋊ D3×C11⋊C5
SylowC11 ⋊ C5×D51
SylowC3 ⋊ D17×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C11×C17C2×C5
LCSG ▷ C3×C11×C17
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD51×AGL(1,𝔽11), D51⋊AGL(1,𝔽11), D3×D17×C11⋊C5, …
maximal normal subgroup ofD51×AGL(1,𝔽11), D51⋊AGL(1,𝔽11), D3×D17×C11⋊C5, …
maximal quotient ofC11⋊C5×Dic51, C2×C11⋊C5×D51, C11⋊C5×D153, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5610, 22);