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C7×C8×AGL(1,𝔽5) #11764643

order1120
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C7×C8 · Schur multiplier (H2) = C4

Aliases

direct productC7×C8×AGL(1,𝔽5)

Splittings

FittingC5×C7×C8 ⋊ C4
derived, SylowC5 ⋊ C4×C7×C8
HallC5×C7 ⋊ C4×C8

Subgroups

subgroupG/H
center, hypercenterC7×C8AGL(1,𝔽5)
commutator, hypocenterC5C4×C7×C8
FrattiniC4C2×C7×AGL(1,𝔽5)
FittingC5×C7×C8C4
socleC2×C5×C7C42
prime radicalC2×C7×D5C2×C4
cosocleC4×D5C22×C7
LCSG ▷ C5
UCSC1 ◁ C7×C8

88 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 ofC7×AGL(1,𝔽5)×AGL(1,𝔽9), C8×AGL(1,𝔽5)×ΓL(1,𝔽8), C8×D7×AGL(1,𝔽5), …
maximal normal subgroup ofC8×AGL(1,𝔽5)×ΓL(1,𝔽8), C8×D7×AGL(1,𝔽5), C7×M16×AGL(1,𝔽5), …
maximal quotient ofC7×AGL(1,𝔽5)×AGL(1,𝔽9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 249);