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C2×AGL(1,𝔽5)×#97 #13033099

order1280
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×AGL(1,𝔽5)×#97

Splittings

FittingC2×C5×#97 ⋊ C4
SylowC5 ⋊ C2×C4×#97

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C2×C43
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#97C4
socleC23×C5C2×C42
prime radicalC23×D5C22×C4
cosocleC2×C4×D5C24
hypercenterC2×#97AGL(1,𝔽5)
hypocenterC5C2×C4×#97
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×#97

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#442, C2×AGL(1,𝔽5)×#347, C2×AGL(1,𝔽5)×#444, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#442, C2×AGL(1,𝔽5)×#347, C2×AGL(1,𝔽5)×#444, …
maximal quotient ofC2×AGL(1,𝔽5)×#347, C2×#97×#1043, C2×#72220669, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103367);