Finite Group Databasebeta

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C22×C11×#63271 #26046581

order12012
isoclinismisoclinic class of #63271
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×C11×#63271

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22×C11#63271
commutator, cosocle, hypocenterC7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C22×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×A4×#63271, C11×#63271⋊A4, C22×C11×ΓL(1,𝔽8)×C13⋊C3, …
maximal normal subgroup ofC11×A4×#63271, C11×#63271⋊A4, C22×C11×ΓL(1,𝔽8)×C13⋊C3, …
maximal quotient ofC22×C11×#11717942, C2×D3×C11×#63271, C22×C3×C11×#63271

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 171);