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D3×ΓL(1,𝔽8)2 #72222191

order2646
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productD3×ΓL(1,𝔽8)2

Splittings

Fitting, socle, derivedC3×C72 ⋊ C2×C32
HallC3×ΓL(1,𝔽8)2 ⋊ C2
SylowC72 ⋊ C32×D3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72C2×C32
LCSG ▷ C3×C72
UCSC1

146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)2×S4, D3×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #72224666, …
maximal normal subgroup ofD3×ΓL(1,𝔽8)⋊AGL(1,𝔽7), C3×D3×ΓL(1,𝔽8)2, D3×ΓL(1,𝔽8)×AGL(1,𝔽7), …
maximal quotient ofΓL(1,𝔽8)2×S4, #72224666, C3⋊D3×ΓL(1,𝔽8)2, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.