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C2×AGL(1,𝔽5)×#135 #13044730

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×AGL(1,𝔽5)×#135
unambiguous semidirect productD5⋊(C4×#135)

Splittings

FittingC2×C5×#135 ⋊ C4
SylowC5 ⋊ C2×C4×#135

Subgroups

subgroupG/H
centerC2×C4D4×AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC2×C5×#135C4
socleC22×C5C2×C4×D4
prime radicalC2×D5×#135C2
cosocleC4×D5C25
hypercenterC2×#135AGL(1,𝔽5)
hypocenterC5C2×C4×#135
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#444, C2×AGL(1,𝔽5)×#509, C2×AGL(1,𝔽5)×#360, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#444, C2×AGL(1,𝔽5)×#509, C2×AGL(1,𝔽5)×#360, …
maximal quotient ofC2×#72220867, C2×#135×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114998);