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AGL(1,𝔽5)×#1369 #72242104

order2560
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productAGL(1,𝔽5)×#1369

Splittings

FittingC5×#1369 ⋊ C4
SylowC5 ⋊ C4×#1369

Subgroups

subgroupG/H
centerC4AGL(1,𝔽5)×#106
commutatorC5×C8C2×C4×C8
FrattiniC4×C8C22×AGL(1,𝔽5)
FittingC5×#1369C4
socleC2×C5C4×#334
prime radicalC22×D5C2×#108
cosocleC4×C8×D5C23
hypercenter#1369AGL(1,𝔽5)
hypocenterC5C4×#1369
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #1369

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#12068, AGL(1,𝔽5)×#7457, AGL(1,𝔽5)×#7390
maximal normal subgroup ofAGL(1,𝔽5)×#12068, AGL(1,𝔽5)×#7457, AGL(1,𝔽5)×#7390

GAP

Past the SmallGroups library coverage — no SmallGroups id.