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C11×C5⋊#64425 #30633551

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C7

Aliases

direct productC11×C5⋊#64425
unambiguous semidirect productC5⋊(C11×#64425)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C11
HallC5×C11×#3862 ⋊ C2
HallC11×C5⋊(C7⋊D7) ⋊ C3
HallC11×#3862 ⋊ D5
HallC5×#3862 ⋊ C2×C11
HallC72×C11 ⋊ C3×D5
HallC5⋊(C7⋊D7) ⋊ C3×C11
Hall#3862 ⋊ D5×C11
HallC5×C11 ⋊ #64425
SylowC72 ⋊ C3×D5×C11
SylowC5 ⋊ C11×#64425

Subgroups

subgroupG/H
center, hypercenterC11C5⋊#64425
commutator, cosocle, hypocenterC5×C72C2×C3×C11
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×#15668774, C11⋊#15668774, C11×#64418⋊D5, …
maximal normal subgroup ofC11×#15668774, C11⋊#15668774, C11×#64418⋊D5, …
maximal quotient ofC11×#15668735, C2×C11×C5⋊#64425

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 96);