Finite Group Databasebeta

← Prev (#72217344) Next (#72217346) →

C2×AGL(1,𝔽7)×AGL(1,𝔽9) #72217345

order6048
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×AGL(1,𝔽7)×AGL(1,𝔽9)

Splittings

Fitting, socleC2×C32×C7 ⋊ C2×C3×C8
derivedC32×C7 ⋊ C22×C3×C8
HallC32×ΓL(1,𝔽8) ⋊ C22×C8
SylowC7 ⋊ C22×C3×AGL(1,𝔽9)

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽7)×AGL(1,𝔽9)
commutator, hypocenterC32×C7C22×C3×C8
FrattiniC1G
Fitting, socleC2×C32×C7C2×C3×C8
prime radicalC2×C3⋊D3×AGL(1,𝔽7)C4
cosocleC7×#157C23×C3
LCSG ▷ C32×C7
UCSC1 ◁ C2

388 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 99 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

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AGL(1,𝔽7)×AGL(1,𝔽9), AGL(1,𝔽7)×D5⋊AGL(1,𝔽9), C4×AGL(1,𝔽7)×AGL(1,𝔽9), …
maximal normal subgroup ofC4×AGL(1,𝔽7)×AGL(1,𝔽9), C2×AGL(1,𝔽7)×AΓL(1,𝔽9)
maximal quotient ofD5×AGL(1,𝔽7)×AGL(1,𝔽9), AGL(1,𝔽7)×D5⋊AGL(1,𝔽9), C4×AGL(1,𝔽7)×AGL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.