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C2×C4×C7×AGL(1,𝔽5) #11765345

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

Aliases

direct productC2×C4×C7×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C42×C7)

Splittings

FittingC2×C4×C5×C7 ⋊ C4
derived, SylowC5 ⋊ C2×C42×C7
HallC5×C7 ⋊ C2×C42

Subgroups

subgroupG/H
center, hypercenterC2×C4×C7AGL(1,𝔽5)
commutator, hypocenterC5C2×C42×C7
FrattiniC2C22×C7×AGL(1,𝔽5)
FittingC2×C4×C5×C7C4
socleC22×C5×C7C2×C4
prime radicalC22×C7×D5C22
cosocleC2×D5C23×C7
LCSG ▷ C5
UCSC1 ◁ C2×C4×C7

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 280

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C4×AGL(1,𝔽5)×ΓL(1,𝔽8), C2×C4×D7×AGL(1,𝔽5), C2×C7×D4×AGL(1,𝔽5), …
maximal normal subgroup ofC2×C4×AGL(1,𝔽5)×ΓL(1,𝔽8), C2×C4×D7×AGL(1,𝔽5), C2×C7×D4×AGL(1,𝔽5), …
maximal quotient ofC7×M16×AGL(1,𝔽5), C7×C22⋊C4×AGL(1,𝔽5), C22×C4×C7×AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 951);