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C11⋊C5×#64424 #30633497

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

Aliases

direct productC11⋊C5×#64424
unambiguous semidirect product(C11×#64424)⋊C5

Splittings

Fitting, socle, derived, HallC72×C11 ⋊ C2×C3×C5
HallC11⋊C5×#3861 ⋊ C2
HallC11⋊C5×C7⋊D7 ⋊ C3
HallC11×#64424 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC11×#3861 ⋊ C2×C5
HallC11×C7⋊D7 ⋊ C3×C5
Hall#3861 ⋊ C2×C11⋊C5
HallC7⋊D7 ⋊ C3×C11⋊C5
SylowC72 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C5×#64424

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 539

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C11⋊C5)⋊(#5997⋊C3), C11⋊C5×#5997⋊C3, AGL(1,𝔽11)×#64424, …
maximal normal subgroup of(C11⋊C5)⋊(#5997⋊C3), C11⋊C5×#5997⋊C3, AGL(1,𝔽11)×#64424, …
maximal quotient ofC11⋊C5×#10596874, C2×C11⋊C5×#64424

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 42);