Finite Group Databasebeta

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C2×C11⋊C5×C49⋊C3 #30633459

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11⋊C5×C49⋊C3
unambiguous semidirect product(C2×C11)⋊(C5×C49⋊C3)
unambiguous semidirect product(C2×C49)⋊(C3×C11⋊C5)
unambiguous semidirect product(C2×C11×C49⋊C3)⋊C5
unambiguous semidirect product(C2×C49×C11⋊C5)⋊C3

Splittings

Fitting, HallC2×C11×C49 ⋊ C3×C5
derived, HallC11×C49 ⋊ C2×C3×C5
HallC2×C49×C11⋊C5 ⋊ C3
HallC2×C11×C49⋊C3 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×C3
HallC11×C49⋊C3 ⋊ C2×C5
HallC2×C49 ⋊ C3×C11⋊C5
SylowC49 ⋊ C2×C3×C11⋊C5
HallC2×C11 ⋊ C5×C49⋊C3
SylowC11 ⋊ C2×C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×C49⋊C3
commutator, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7C2×ΓL(1,𝔽8)×C11⋊C5
FittingC2×C11×C49C3×C5
socleC2×C7×C11C5×ΓL(1,𝔽8)
LCSG ▷ C11×C49
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1078

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC4×C11⋊C5×C49⋊C3, C49⋊C3×Dic11⋊C5, C11⋊C5×(C49⋊C3)⋊C4, …
maximal normal subgroup ofC4×C11⋊C5×C49⋊C3, C49⋊C3×Dic11⋊C5, C11⋊C5×(C49⋊C3)⋊C4, …
maximal quotient ofC4×C11⋊C5×C49⋊C3, C22×C11⋊C5×C49⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 4);