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C5×C22⋊C4×AGL(1,𝔽7) #72218139

order3360
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×C22⋊C4×AGL(1,𝔽7)

Splittings

FittingC5×C7×C22⋊C4 ⋊ C2×C3
HallC5×D7×C22⋊C4 ⋊ C3
HallD7×C22⋊C4 ⋊ C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×C22⋊C4
HallC5×C7 ⋊ C2×C3×C22⋊C4
HallΓL(1,𝔽8) ⋊ C2×C5×C22⋊C4
SylowC7 ⋊ C2×C3×C5×C22⋊C4

Subgroups

subgroupG/H
centerC22×C5C22×AGL(1,𝔽7)
commutatorC2×C7C22×C3×C4×C5
FrattiniC22C22×C5×AGL(1,𝔽7)
FittingC5×C7×C22⋊C4C2×C3
socleC22×C5×C7C23×C3
prime radicalC23×C5×AGL(1,𝔽7)C2
cosocleC22×C7C23×C3×C5
hypercenterC5×C22⋊C4AGL(1,𝔽7)
hypocenterC7C2×C3×C5×C22⋊C4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C5 ◁ C5×C22⋊C4

528 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

350 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD5×C22⋊C4×AGL(1,𝔽7), C5×#120×AGL(1,𝔽7), AGL(1,𝔽7)×#4028
maximal normal subgroup ofD5×C22⋊C4×AGL(1,𝔽7), C5×#120×AGL(1,𝔽7), AGL(1,𝔽7)×#4028

GAP

Past the SmallGroups library coverage — no SmallGroups id.