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D4×#3995 #13040296

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

Aliases

direct productD4×#3995

Splittings

SylowC5 ⋊ D4×#108

Subgroups

subgroupG/H
centerC22C22×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×C8×D4C4
socleC22×C5C22×C4⋊C4
prime radicalC2×D4×D5Q8
cosocleC2×C4×D5C24
hypercenterC8×D4AGL(1,𝔽5)
hypocenterC5D4×#108
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1110564);