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Q16×C4⋊AGL(1,𝔽5) #13040324

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

Aliases

direct productQ16×C4⋊AGL(1,𝔽5)

Splittings

FittingC4×C5×Q16 ⋊ C4
SylowC5 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×Q16C4
socleC22×C5C2×C4×D4
prime radicalC22×D5C22×D4
cosocleC2×C4×D5C24
hypercenterC4×Q16AGL(1,𝔽5)
hypocenterC5C4⋊C4×Q16
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1110592);