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C22×AGL(1,𝔽29) #72218684

order3248
automorphism?
homologyAbelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23

Aliases

direct productC22×AGL(1,𝔽29)

Splittings

Fitting, socleC22×C29 ⋊ C4×C7
derived, SylowC29 ⋊ C22×C4×C7
HallC22×#1181 ⋊ C7
HallC29⋊C7 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22AGL(1,𝔽29)
commutator, hypocenterC29C22×C4×C7
FrattiniC1G
Fitting, socleC22×C29C4×C7
prime radicalC22×D29⋊C7C2
cosocleD29C23×C7
LCSG ▷ C29
UCSC1 ◁ C22

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C4×AGL(1,𝔽29), C23×AGL(1,𝔽29), C2×D5×AGL(1,𝔽29), …
maximal normal subgroup ofC2×C4×AGL(1,𝔽29), C23×AGL(1,𝔽29), C22×C5×AGL(1,𝔽29), …
maximal quotient ofC2×C4×AGL(1,𝔽29), C23×AGL(1,𝔽29), C2×D5×AGL(1,𝔽29), …
automorphism group of#6597, C4×D29, C22⋊D29

GAP

Past the SmallGroups library coverage — no SmallGroups id.