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C22×C3×C43⋊C3 #13095445

order1548
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C43⋊C3

Splittings

Fitting, socleC22×C3×C43 ⋊ C3
derived, SylowC43 ⋊ C22×C32
HallC22×C43 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC22×C3C43⋊C3
commutator, cosocle, hypocenterC43C22×C32
FrattiniC1G
Fitting, socleC22×C3×C43C3
LCSG ▷ C43
UCSC1 ◁ C22×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 516

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C3×(C43⋊C3)⋊C7, C2×AGL(1,𝔽7)×C43⋊C3, C22×ΓL(1,𝔽8)×C43⋊C3, …
maximal normal subgroup ofC22×C3×(C43⋊C3)⋊C7, C22×C3×C7×C43⋊C3, C22×C3×C11×C43⋊C3, …
maximal quotient ofC2×AGL(1,𝔽7)×C43⋊C3, C22×ΓL(1,𝔽8)×C43⋊C3, C2×C3×#14268592, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1548, 38);