Finite Group Databasebeta

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C2×C4×AGL(1,𝔽31) #72219366

order7440
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×AGL(1,𝔽31)

Splittings

FittingC2×C4×C31 ⋊ C2×C3×C5
derived, SylowC31 ⋊ C22×C3×C4×C5
HallC2×C4×D31⋊C5 ⋊ C3
HallC2×C4×D31⋊C3 ⋊ C5
HallC2×C4×D31 ⋊ C3×C5
Hall(C31⋊C3)⋊C5 ⋊ C22×C4
HallΓL(1,𝔽32) ⋊ C22×C3×C4
HallC31⋊C3 ⋊ C22×C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C4AGL(1,𝔽31)
commutator, hypocenterC31C22×C3×C4×C5
FrattiniC2C22×AGL(1,𝔽31)
FittingC2×C4×C31C2×C3×C5
socleC22×C31C22×C3×C5
prime radicalC22×AGL(1,𝔽31)C2
cosocleC2×C31C23×C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C4

216 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 116 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

248 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D3×AGL(1,𝔽31), C2×C3×C4×AGL(1,𝔽31), C2×C4×C3⋊AGL(1,𝔽31), …
maximal normal subgroup ofC2×C3×C4×AGL(1,𝔽31), C22×C4×AGL(1,𝔽31), C2×D4×AGL(1,𝔽31), …
maximal quotient ofC4×D3×AGL(1,𝔽31), C2×C3×C4×AGL(1,𝔽31), C2×C4×C3⋊AGL(1,𝔽31), …

GAP

Past the SmallGroups library coverage — no SmallGroups id.