Finite Group Databasebeta

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C2×C3×C53×C11⋊C5 #31775807

order17490
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C53 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C53×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C3×C5×C53)
unambiguous semidirect product(C2×C3×C11)⋊(C5×C53)
unambiguous semidirect product(C2×C11×C53)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C11×C53)⋊C5

Splittings

Fitting, socle, HallC2×C3×C11×C53 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C5×C53
HallC3×C11×C53 ⋊ C2×C5
HallC2×C11×C53 ⋊ C3×C5
HallC11×C53 ⋊ C2×C3×C5
HallC2×C3×C11 ⋊ C5×C53
HallC3×C11 ⋊ C2×C5×C53
HallC2×C11 ⋊ C3×C5×C53

Subgroups

subgroupG/H
center, hypercenterC2×C3×C53C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C5×C53
FrattiniC1G
Fitting, socleC2×C3×C11×C53C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3498

Conjugacy classes & character table

2226 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C53×C11⋊C5, C3×C11⋊C5×Dic53, C3×C53×Dic11⋊C5, …
maximal normal subgroup ofC3×C4×C53×C11⋊C5, C3×C11⋊C5×Dic53, C3×C53×Dic11⋊C5, …
maximal quotient ofC3×C4×C53×C11⋊C5, C22×C3×C53×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 2);