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C2×#10598528 #13015879

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10598528

Splittings

FittingC2×C4×C5×C8 ⋊ C4
SylowC5 ⋊ C2×#1288

Subgroups

subgroupG/H
centerC23(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C2×C42
FrattiniC42C22×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socleC23×C5#95
prime radicalC23×D5C22⋊C4
cosocleC42×D5C23
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C2×#1288
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 1086147);