Finite Group Databasebeta

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A42×AGL(1,𝔽7) #72222209

order6048
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C22×C33

Aliases

direct productA42×AGL(1,𝔽7)

Splittings

Fitting, socle, derivedC24×C7 ⋊ C2×C33
HallC24×D7 ⋊ C33
SylowC7 ⋊ C2×C3×A42

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC24×C7C2×C33
LCSG ▷ C24×C7
UCSC1

824 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 95 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

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×A4⋊S4, #72222333, A4×S4×AGL(1,𝔽7), …
maximal normal subgroup ofAGL(1,𝔽7)×A4⋊S4, A4×S4×AGL(1,𝔽7), C2×A42×AGL(1,𝔽7)
maximal quotient of#72222333, C2×A42×AGL(1,𝔽7), AGL(1,𝔽7)×Ω+(4,𝔽3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.