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D5×C11×C49⋊C3 #30633485

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11×C49⋊C3
unambiguous semidirect productC5⋊(C2×C11×C49⋊C3)
unambiguous semidirect product(D5×C49)⋊(C3×C11)
unambiguous semidirect product(D5×C11×C49)⋊C3

Splittings

Fitting, HallC5×C11×C49 ⋊ C2×C3
derived, HallC5×C49 ⋊ C2×C3×C11
HallC5×C11×C49⋊C3 ⋊ C2
HallD5×C11×C49 ⋊ C3
HallC5×C49⋊C3 ⋊ C2×C11
HallC11×C49 ⋊ C3×D5
HallD5×C49 ⋊ C3×C11
HallC5×C11 ⋊ C2×C49⋊C3
SylowC49 ⋊ C3×D5×C11
SylowC5 ⋊ C2×C11×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC11D5×C49⋊C3
commutator, cosocle, hypocenterC5×C49C2×C3×C11
FrattiniC7D5×C11×ΓL(1,𝔽8)
FittingC5×C11×C49C2×C3
socleC5×C7×C11C2×ΓL(1,𝔽8)
LCSG ▷ C5×C49
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×(C49⋊C3)⋊AGL(1,𝔽5), C11⋊((C49⋊C3)⋊AGL(1,𝔽5)), C11×AGL(1,𝔽5)×C49⋊C3, …
maximal normal subgroup ofC11×(C49⋊C3)⋊AGL(1,𝔽5), C11⋊((C49⋊C3)⋊AGL(1,𝔽5)), C11×AGL(1,𝔽5)×C49⋊C3, …
maximal quotient ofC11×Dic5×C49⋊C3, C2×D5×C11×C49⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 30);