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C2×C32×C7×C11⋊C5 #20294185

order6930
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC2×C32×C7×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C32×C5×C7)
unambiguous semidirect product(C2×C3×C11)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C32×C11)⋊(C5×C7)
unambiguous semidirect product(C2×C32×C7×C11)⋊C5

Splittings

Fitting, socle, HallC2×C32×C7×C11 ⋊ C5
derived, SylowC11 ⋊ C2×C32×C5×C7
HallC32×C7×C11 ⋊ C2×C5
HallC2×C32×C11 ⋊ C5×C7
HallC2×C7×C11 ⋊ C32×C5
HallC32×C11 ⋊ C2×C5×C7
HallC7×C11 ⋊ C2×C32×C5
HallC2×C11 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C32×C7C11⋊C5
commutator, hypocenterC11C2×C32×C5×C7
FrattiniC1G
Fitting, socleC2×C32×C7×C11C5
LCSG ▷ C11
UCSC1 ◁ C2×C32×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

882 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×C7×Dic11⋊C5, C32×C7⋊(Dic11⋊C5), C32×Dic7×C11⋊C5, …
maximal normal subgroup ofC32×C7×Dic11⋊C5, C32×C7⋊(Dic11⋊C5), C32×Dic7×C11⋊C5, …
maximal quotient ofC32×C4×C7×C11⋊C5, C22×C32×C7×C11⋊C5, C2×C32×C7×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 72);