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D4×#3992 #13033780

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productD4×#3992

Splittings

FittingC5×C8×D4 ⋊ C4
SylowC5 ⋊ D4×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C22×C42
FittingC5×C8×D4C4
prime radicalC2×D4×D5C2×C4
cosocleC2×C4×D5C24
hypercenterC8×D4AGL(1,𝔽5)
hypocenterC5D4×#97
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C8×D4

1274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2970, #72269248
maximal normal subgroup ofAGL(1,𝔽5)×#2970, #72269248

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1104048);