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C2×#10604912 #13030296

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#10604912

Splittings

FittingC23×C5×D4 ⋊ C4
SylowC5 ⋊ C2×#1510

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC23×C5×D4C4
socleC23×C5C2×C22⋊C4
prime radicalC22×#4084C2
cosocleC2×C4×D5C24
hypercenterC23×D4AGL(1,𝔽5)
hypocenterC5C2×#1510
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1100564);