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C2×#120×AGL(1,𝔽7) #72218557

order2688
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C211

Aliases

direct productC2×#120×AGL(1,𝔽7)

Splittings

FittingC2×C7×#120 ⋊ C2×C3
HallC2×D7×#120 ⋊ C3
HallΓL(1,𝔽8) ⋊ C22×#120
SylowC7 ⋊ C22×C3×#120

Subgroups

subgroupG/H
centerC23C23×AGL(1,𝔽7)
commutator, cosocleC22×C7C25×C3
FrattiniC22C24×AGL(1,𝔽7)
FittingC2×C7×#120C2×C3
socleC23×C7C24×C3
hypercenterC2×#120AGL(1,𝔽7)
hypocenterC7C22×C3×#120
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#120

9088 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#120×AGL(1,𝔽7), C4×#120×AGL(1,𝔽7), D3×#120×AGL(1,𝔽7), …
maximal normal subgroup ofC4×#120×AGL(1,𝔽7), C2×AGL(1,𝔽7)×B(4,𝔽2), AGL(1,𝔽7)×#3484, …
maximal quotient ofD5×#120×AGL(1,𝔽7), C4×#120×AGL(1,𝔽7), D3×#120×AGL(1,𝔽7), …
automorphism group ofC4⋊(C7⋊C8), C8×Dic7, #6389, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.