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C11×C22⋊#63270 #26046575

order12012
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C22⋊#63270
unambiguous semidirect productC22⋊(C11×#63270)
unambiguous semidirect product(C22×C11)⋊#63270

Splittings

Fitting, socle, HallC22×C7×C11×C13 ⋊ C3
derived, HallC22×C7×C13 ⋊ C3×C11
HallC7×C11×C13 ⋊ A4
HallC22×C11×C13 ⋊ ΓL(1,𝔽8)
HallC22×C7×C11 ⋊ C13⋊C3
HallC11×C13 ⋊ C22⋊ΓL(1,𝔽8)
HallC7×C13 ⋊ C11×A4
HallC7×C11 ⋊ C22⋊(C13⋊C3)
HallC22×C13 ⋊ C11×ΓL(1,𝔽8)
HallC22×C11 ⋊ #63270
HallC22×C7 ⋊ C11×C13⋊C3
SylowC13 ⋊ C11×C22⋊ΓL(1,𝔽8)
SylowC7 ⋊ C11×C22⋊(C13⋊C3)
SylowC22 ⋊ C11×#63270

Subgroups

subgroupG/H
center, hypercenterC11C22⋊#63270
commutator, cosocle, hypocenterC22×C7×C13C3×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C13C3
LCSG ▷ C22×C7×C13
UCSC1 ◁ C11

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×C13⋊C3×C22⋊ΓL(1,𝔽8), C11×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C11×A4×#63270, …
maximal normal subgroup ofC11×C13⋊C3×C22⋊ΓL(1,𝔽8), C11×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C11×A4×#63270, …
maximal quotient ofC11×C22⋊#11717941, C3×C11×C22⋊#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 165);