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C11×C5⋊#64422 #30633555

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

Aliases

direct productC11×C5⋊#64422
unambiguous semidirect productC5⋊(C11×#64422)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C11
HallC5×C11×#3862 ⋊ C2
HallC7×C11×D35 ⋊ C3
HallC11×#3862 ⋊ D5
HallC5×#3862 ⋊ C2×C11
HallC72×C11 ⋊ C3×D5
HallC7×D35 ⋊ C3×C11
Hall#3862 ⋊ D5×C11
HallC5×C11 ⋊ #64422
SylowC72 ⋊ C3×D5×C11
SylowC5 ⋊ C11×#64422

Subgroups

subgroupG/H
center, hypercenterC11C5⋊#64422
commutator, cosocle, hypocenterC5×C72C2×C3×C11
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C11

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD11×C5⋊#64422, D5×C11×#64422, D55⋊#64422, …
maximal normal subgroup ofD11×C5⋊#64422, D5×C11×#64422, D55⋊#64422, …
maximal quotient ofC11×#15668737, C2×C11×C5⋊#64422

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 100);