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AGL(1,𝔽5)×C22⋊C16 #13025669

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productAGL(1,𝔽5)×C22⋊C16

Splittings

FittingC5×C22⋊C16 ⋊ C4
SylowC5 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C16
FittingC5×C22⋊C16C4
socleC22×C5C2×C4×C8
prime radicalC23×D5C2×C8
cosocleC2×C8×D5C23
hypercenterC22⋊C16AGL(1,𝔽5)
hypocenterC5C4×C22⋊C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22⋊C16

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1095937);