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D3×A4×AGL(1,𝔽7) #72222271

order3024
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3

Aliases

direct productD3×A4×AGL(1,𝔽7)

Splittings

Fitting, socle, derivedC22×C3×C7 ⋊ C22×C32
SylowC7 ⋊ C2×C3×D3×A4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C3×C7C22×C32
LCSG ▷ C22×C3×C7
UCSC1

464 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×S4×AGL(1,𝔽7), A4×S4×AGL(1,𝔽7), C2×D3×A4×AGL(1,𝔽7)
maximal normal subgroup ofD3×S4×AGL(1,𝔽7), C2×D3×A4×AGL(1,𝔽7)
maximal quotient ofA4×S4×AGL(1,𝔽7), C2×D3×A4×AGL(1,𝔽7), D3×SL(2,𝔽3)×AGL(1,𝔽7)
automorphism group ofC3×C22⋊ΓL(1,𝔽8)

GAP

Past the SmallGroups library coverage — no SmallGroups id.