Finite Group Databasebeta

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C2×C32×C5×C7×D11 #28357797

order13860
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C22×C32×C5×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C5×C7×D11

Splittings

Fitting, socleC2×C32×C5×C7×C11 ⋊ C2
derived, SylowC11 ⋊ C22×C32×C5×C7
HallC32×C5×C7×C11 ⋊ C22
HallC32×C7×C11 ⋊ C22×C5
HallC32×C5×C11 ⋊ C22×C7
HallC5×C7×C11 ⋊ C22×C32
HallC32×C11 ⋊ C22×C5×C7
HallC7×C11 ⋊ C22×C32×C5
HallC5×C11 ⋊ C22×C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5×C7D11
commutator, cosocle, hypocenterC11C22×C32×C5×C7
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C11C2
LCSG ▷ C11
UCSC1 ◁ C2×C32×C5×C7

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6930

Conjugacy classes & character table

4410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 464);