Finite Group Databasebeta

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C2×C3×C72×C11⋊C5 #30633567

order16170
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC2×C3×C72×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C3×C5×C72)
unambiguous semidirect product(C2×C3×C11)⋊(C5×C72)
unambiguous semidirect product(C2×C3×C7×C11)⋊(C5×C7)
unambiguous semidirect product(C2×C3×C72×C11)⋊C5

Splittings

Fitting, socle, HallC2×C3×C72×C11 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C5×C72
HallC3×C72×C11 ⋊ C2×C5
HallC2×C72×C11 ⋊ C3×C5
HallC72×C11 ⋊ C2×C3×C5
HallC2×C3×C11 ⋊ C5×C72
HallC3×C11 ⋊ C2×C5×C72
HallC2×C11 ⋊ C3×C5×C72

Subgroups

subgroupG/H
center, hypercenterC2×C3×C72C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C5×C72
FrattiniC1G
Fitting, socleC2×C3×C72×C11C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3234

Conjugacy classes & character table

2058 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C72×Dic11⋊C5, C3×C7×C7⋊(Dic11⋊C5), C3×C7×Dic7×C11⋊C5, …
maximal normal subgroup ofC3×C72×Dic11⋊C5, C3×C7×C7⋊(Dic11⋊C5), C3×C7×Dic7×C11⋊C5, …
maximal quotient ofC3×C4×C72×C11⋊C5, C22×C3×C72×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 112);