Finite Group Databasebeta

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C2×AGL(1,𝔽5)×#347 #72242348

order2560
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC2×AGL(1,𝔽5)×#347

Splittings

FittingC2×C5×#347 ⋊ C4
SylowC5 ⋊ C2×C4×#347

Subgroups

subgroupG/H
centerC2×C4C42×AGL(1,𝔽5)
commutatorC4×C5C2×C43
FrattiniC2×C8C23×AGL(1,𝔽5)
FittingC2×C5×#347C4
socleC22×C5C4×#97
prime radicalC23×D5C2×M16
cosocleC2×C8×D5C24
hypercenterC2×#347AGL(1,𝔽5)
hypocenterC5C2×C4×#347
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×#347

2076 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×AGL(1,ℤ/16), C2×#347×#1043
maximal normal subgroup ofC2×AGL(1,𝔽5)×AGL(1,ℤ/16)
maximal quotient ofC2×#347×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.