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C2×AGL(1,𝔽5)×#104 #13033397

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×AGL(1,𝔽5)×#104

Splittings

FittingC2×C5×#104 ⋊ C4
SylowC5 ⋊ C2×C4×#104

Subgroups

subgroupG/H
centerC2×C4D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#104C4
socleC22×C5C4×C22⋊C4
prime radicalC2×D5×#41C22
cosocleC2×C4×D5C24
hypercenterC2×#104AGL(1,𝔽5)
hypocenterC5C2×C4×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

1878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72213321, C2×#104×#1043, AGL(1,𝔽5)×#2002, …
maximal normal subgroup ofAGL(1,𝔽5)×#2002, AGL(1,𝔽5)×#1906, C2×AGL(1,𝔽5)×#453, …
maximal quotient ofC2×#72213321, C2×#104×#1043, D3×AGL(1,𝔽5)×#104, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103665);