Finite Group Databasebeta

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C2×C32×C11×C11⋊C5 #24926193

order10890
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC2×C32×C11×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C32×C5×C11)
unambiguous semidirect product(C2×C3×C11)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C32×C11)⋊(C5×C11)

Splittings

Fitting, socle, HallC2×C32×C112 ⋊ C5
derivedC11 ⋊ C2×C32×C5×C11
HallC32×C112 ⋊ C2×C5
HallC2×C112 ⋊ C32×C5
SylowC112 ⋊ C2×C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11C11⋊C5
commutator, cosocle, hypocenterC11C2×C32×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C112C5
LCSG ▷ C11
UCSC1 ◁ C2×C32×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C11×Dic11⋊C5, C32×(C11⋊C5)⋊Dic11, C32×Dic11×C11⋊C5, …
maximal normal subgroup ofC32×C11×Dic11⋊C5, C32×(C11⋊C5)⋊Dic11, C32×Dic11×C11⋊C5, …
maximal quotient ofC32×C4×C11×C11⋊C5, C22×C32×C11×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 142);