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D4×D5⋊M16 #13044669

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×D5⋊M16
unambiguous semidirect productD5⋊(D4×M16)

Splittings

SylowC5 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
prime radicalC22×D4×D5C4
cosocleC2×Dic5C25
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5C2×D4×M16
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

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, 1114937);