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C2×#10604386 #13033204

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#10604386

Splittings

SylowC5 ⋊ C22×#344

Subgroups

subgroupG/H
centerC2×C4(C2×AGL(1,𝔽5))⋊C4
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C5×#117C4
socleC22×C5C2×#95
prime radicalC24×D5C2×C4
cosocleC22×Dic5C24
hypercenterC2×#117AGL(1,𝔽5)
hypocenterC5C22×#344
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

2190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103472);