Finite Group Databasebeta

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C4×C5×C7×AGL(1,𝔽5) #72219065

order2800
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C42×C5×C7 · Schur multiplier (H2) = C4

Aliases

direct productC4×C5×C7×AGL(1,𝔽5)

Splittings

FittingC4×C52×C7 ⋊ C4
derivedC5 ⋊ C42×C5×C7
HallC52×C7 ⋊ C42
SylowC52 ⋊ C42×C7

Subgroups

subgroupG/H
center, hypercenterC4×C5×C7AGL(1,𝔽5)
commutator, hypocenterC5C42×C5×C7
FrattiniC2C2×C5×C7×AGL(1,𝔽5)
FittingC4×C52×C7C4
socleC2×C52×C7C2×C4
prime radicalC2×C5×C7×D5C22
cosocleC2×D5C22×C5×C7
LCSG ▷ C5
UCSC1 ◁ C4×C5×C7

126 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC4×C5×AGL(1,𝔽5)×ΓL(1,𝔽8), C4×C5×D7×AGL(1,𝔽5)
maximal normal subgroup ofC4×C5×AGL(1,𝔽5)×ΓL(1,𝔽8), C4×C5×D7×AGL(1,𝔽5)

GAP

Past the SmallGroups library coverage — no SmallGroups id.