Finite Group Databasebeta

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C2×C3×C5×C11×C11⋊C5 #31827698

order18150
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC2×C3×C5×C11×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C3×C52×C11)
unambiguous semidirect product(C2×C3×C11)⋊(C52×C11)
unambiguous semidirect product(C2×C5×C11)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C3×C5×C11)⋊(C5×C11)

Splittings

Fitting, socleC2×C3×C5×C112 ⋊ C5
derivedC11 ⋊ C2×C3×C52×C11
HallC2×C3×C112 ⋊ C52
HallC3×C112 ⋊ C2×C52
HallC2×C112 ⋊ C3×C52
SylowC112 ⋊ C2×C3×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C52×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C112C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C11×Dic11⋊C5, C3×C5×(C11⋊C5)⋊Dic11, C3×C5×Dic11×C11⋊C5, …
maximal normal subgroup ofC3×C5×C11×Dic11⋊C5, C3×C5×(C11⋊C5)⋊Dic11, C3×C5×Dic11×C11⋊C5, …
maximal quotient ofC3×C4×C5×C11×C11⋊C5, C22×C3×C5×C11×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 182);