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C2×AGL(1,𝔽5)×D16 #13043568

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×AGL(1,𝔽5)×D16
unambiguous semidirect productD5⋊(C4×D16)

Splittings

FittingC2×C5×D16 ⋊ C4
SylowC5 ⋊ C2×C4×D16

Subgroups

subgroupG/H
centerC22D8×AGL(1,𝔽5)
commutatorC5×C8C23×C4
FrattiniC8C23×AGL(1,𝔽5)
FittingC2×C5×D16C4
socleC22×C5C4×D8
prime radicalC2×D5×D16C2
cosocleC8×D5C24
hypercenterC2×D16AGL(1,𝔽5)
hypocenterC5C2×C4×D16
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2177, AGL(1,𝔽5)×#2263, AGL(1,𝔽5)×#1419, …
maximal normal subgroup ofAGL(1,𝔽5)×#2177, AGL(1,𝔽5)×#2263, AGL(1,𝔽5)×#1419, …
maximal quotient ofAGL(1,𝔽5)×#2263, C2×D16×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113836);