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ΓL(1,𝔽8)×GL(3,𝔽2) #72209940

order3528
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C2

Aliases

direct productΓL(1,𝔽8)×GL(3,𝔽2)

Splittings

FittingC7 ⋊ C3×GL(3,𝔽2)
socle, derivedC7×GL(3,𝔽2) ⋊ C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, socle, hypocenterC7×GL(3,𝔽2)C3
Fitting, cosocleC7C3×GL(3,𝔽2)
LCSG ▷ C7×GL(3,𝔽2)
UCSC1

74 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofGL(3,𝔽2)2, ΓL(1,𝔽8)×AGL(3,𝔽2), AGL(1,𝔽7)×GL(3,𝔽2), …
maximal normal subgroup ofAGL(1,𝔽7)×GL(3,𝔽2), C2×ΓL(1,𝔽8)×GL(3,𝔽2), #72244479
maximal quotient ofΓL(1,𝔽8)×AGL(3,𝔽2), ΓL(1,𝔽8)×SL(2,𝔽7), C2×ΓL(1,𝔽8)×GL(3,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.