Finite Group Databasebeta

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C22×C7×C11×C13⋊C3 #26046583

order12012
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×C7×C11×C13⋊C3

Splittings

Fitting, socle, HallC22×C7×C11×C13 ⋊ C3
derived, SylowC13 ⋊ C22×C3×C7×C11
HallC7×C11×C13 ⋊ C22×C3
HallC22×C11×C13 ⋊ C3×C7
HallC22×C7×C13 ⋊ C3×C11
HallC11×C13 ⋊ C22×C3×C7
HallC7×C13 ⋊ C22×C3×C11
HallC22×C13 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC22×C7×C11C13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C7×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C7×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C11×A4×C13⋊C3, C11×C13⋊C3×C22⋊ΓL(1,𝔽8), C22×C11×ΓL(1,𝔽8)×C13⋊C3, …
maximal normal subgroup ofC7×C11×A4×C13⋊C3, C11×C13⋊C3×C22⋊ΓL(1,𝔽8), C22×C11×ΓL(1,𝔽8)×C13⋊C3, …
maximal quotient ofC22×C7×C11×C13⋊C9, C2×D3×C7×C11×C13⋊C3, C22×C3×C7×C11×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 173);