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C2×AGL(1,𝔽5)×#101 #13033364

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

Aliases

direct productC2×AGL(1,𝔽5)×#101

Splittings

FittingC2×C5×#101 ⋊ C4
SylowC5 ⋊ C2×C4×#101

Subgroups

subgroupG/H
centerC22C22⋊C4×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#101C4
socleC22×C5C4×C22⋊C4
prime radicalC23×D5C22×C4
cosocleC2×C4×D5C24
hypercenterC2×#101AGL(1,𝔽5)
hypocenterC5C2×C4×#101
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

1538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103632);