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Q8×(C2×AGL(1,𝔽5))⋊C4 #13028020

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

Aliases

direct productQ8×(C2×AGL(1,𝔽5))⋊C4

Splittings

FittingC2×C4×C5×Q8 ⋊ C4
SylowC5 ⋊ Q8×#95

Subgroups

subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC2×C4×C5×Q8C4
socleC23×C5C23×C4
prime radical, cosocleC23×D5C24
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5Q8×#95
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098288);