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C2×AGL(1,𝔽5)×#102 #13033412

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×AGL(1,𝔽5)×#102

Splittings

FittingC2×C5×#102 ⋊ C4
SylowC5 ⋊ C2×C4×#102

Subgroups

subgroupG/H
centerC23D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#102C4
socleC23×C5C4×D4
prime radicalC22×D4×D5C22
cosocleC2×C4×D5C24
hypercenterC2×#102AGL(1,𝔽5)
hypocenterC5C2×C4×#102
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

2158 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)×#442, C2×#102×#1043
maximal normal subgroup ofC2×AGL(1,𝔽5)×#442
maximal quotient ofC2×AGL(1,𝔽5)×#360, C2×AGL(1,𝔽5)×#361, C2×#102×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103680);