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C2×C4×C7⋊AGL(1,𝔽5) #11765358

order1120
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×C7⋊AGL(1,𝔽5)

Splittings

FittingC2×C4×C5×C7 ⋊ C4
derived, HallC5×C7 ⋊ C2×C42
SylowC7 ⋊ C2×C4×AGL(1,𝔽5)
SylowC5 ⋊ C2×C4×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C4C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C2×C42
FrattiniC2C22×C7⋊AGL(1,𝔽5)
FittingC2×C4×C5×C7C4
socleC22×C5×C7C2×C4
prime radicalC22×C7×D5C22
cosocleC2×C7×D5C23
LCSG ▷ C5×C7
UCSC1 ◁ C2×C4

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 280

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C4×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C2×C4×D7×AGL(1,𝔽5), C2×D4×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC2×C4×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C2×C4×D7×AGL(1,𝔽5), C2×D4×C7⋊AGL(1,𝔽5), …
maximal quotient ofM16×C7⋊AGL(1,𝔽5), C22⋊C4×C7⋊AGL(1,𝔽5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 964);