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M16×C22⋊AGL(1,𝔽5) #13033325

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productM16×C22⋊AGL(1,𝔽5)

Splittings

FittingC22×C5×M16 ⋊ C4
SylowC5 ⋊ C22⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C22×C42
FittingC22×C5×M16C4
prime radicalC24×D5C2×C4
cosocleC2×C4×D5C24
hypercenterC22×M16AGL(1,𝔽5)
hypocenterC5C22⋊C4×M16
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×M16

1774 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, 1103593);