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AGL(1,𝔽8)2 #72214170

order3136
automorphism?
homologyAbelianization (H1) = C72 · Schur multiplier (H2) = C7

Aliases

direct productAGL(1,𝔽8)2

Splittings

Fitting, socle, derived, SylowC26 ⋊ C72

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC26C72
LCSG ▷ C26
UCSC1

118 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC2×#72214179, #72244497, AΓL(1,𝔽8)2, …
maximal subgroup of#72214179, C2×AGL(1,𝔽8)2, AGL(1,𝔽8)×AΓL(1,𝔽8), …
maximal normal subgroup of#72214179, C2×AGL(1,𝔽8)2, AGL(1,𝔽8)×AΓL(1,𝔽8), …
maximal quotient ofC2×AGL(1,𝔽8)2, C3×AGL(1,𝔽8)2

GAP

Past the SmallGroups library coverage — no SmallGroups id.