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#120×C5⋊AGL(1,𝔽7) #72218511

order6720
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C27

Aliases

direct product#120×C5⋊AGL(1,𝔽7)

Splittings

FittingC5×C7×#120 ⋊ C2×C3
Hall#120×D35 ⋊ C3
HallC5×ΓL(1,𝔽8) ⋊ C2×#120
HallC5×C7 ⋊ C2×C3×#120
HallΓL(1,𝔽8) ⋊ D5×#120
SylowC7 ⋊ C3×D5×#120
SylowC5 ⋊ #120×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, FrattiniC22C23×C5⋊AGL(1,𝔽7)
commutator, socle, cosocleC22×C5×C7C24×C3
FittingC5×C7×#120C2×C3
hypercenter#120C5⋊AGL(1,𝔽7)
hypocenterC5×C7C2×C3×#120
LCSG ▷ C22×C5×C7 ▷ C5×C7
UCSC1 ◁ C22 ◁ #120

2648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#120×AGL(1,𝔽7)
maximal normal subgroup ofD5×#120×AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.