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AGL(1,𝔽5)×#3018 #72221481

order2560
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productAGL(1,𝔽5)×#3018

Splittings

FittingC5×#3018 ⋊ C4
SylowC5 ⋊ C4×#3018

Subgroups

subgroupG/H
centerC4AGL(1,𝔽5)×#120
commutatorC2×C4×C5C24×C4
FrattiniC2×C4C24×AGL(1,𝔽5)
FittingC5×#3018C4
socleC2×C5C2×C4×#120
prime radicalD5×#3018C2
cosocleC2×C4×D5C25
hypercenter#3018AGL(1,𝔽5)
hypocenterC5C4×#3018
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #3018

9400 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#61110, AGL(1,𝔽5)×#23872
maximal normal subgroup ofAGL(1,𝔽5)×#61110, AGL(1,𝔽5)×#23872

GAP

Past the SmallGroups library coverage — no SmallGroups id.