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C4×D32×AGL(1,𝔽7) #72217530

order6048
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×D32×AGL(1,𝔽7)

Splittings

FittingC32×C4×C7 ⋊ C23×C3
derivedC32×C7 ⋊ C23×C3×C4
HallC32×ΓL(1,𝔽8) ⋊ C23×C4
SylowC7 ⋊ C2×C3×C4×D32

Subgroups

subgroupG/H
center, hypercenterC4D32×AGL(1,𝔽7)
commutator, hypocenterC32×C7C23×C3×C4
FrattiniC2C2×D32×AGL(1,𝔽7)
FittingC32×C4×C7C23×C3
socle, cosocleC2×C32×C7C24×C3
prime radicalC2×D32×AGL(1,𝔽7)C2
LCSG ▷ C32×C7
UCSC1 ◁ C4

2244 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×AGL(1,𝔽7)×GO+(4,𝔽2), D32×AGL(1,𝔽5)×AGL(1,𝔽7), D32×D4×AGL(1,𝔽7), …
maximal normal subgroup ofC4×AGL(1,𝔽7)×GO+(4,𝔽2), D32×D4×AGL(1,𝔽7), AGL(1,𝔽7)×#64312, …
maximal quotient ofD32×AGL(1,𝔽5)×AGL(1,𝔽7)
automorphism group ofC5×D3×D21

GAP

Past the SmallGroups library coverage — no SmallGroups id.