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C2×#10598696 #13015347

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#10598696

Splittings

SylowC5 ⋊ C2×#1276

Subgroups

subgroupG/H
centerC22×C4C4⋊AGL(1,𝔽5)
commutatorC4×C5C2×C4×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC22×C42×C5C4
socleC23×C5#95
prime radicalC24×C5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC22×C42AGL(1,𝔽5)
hypocenterC5C2×#1276
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1085615);