Finite Group Databasebeta

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C5×AGL(1,𝔽5)×#453 #72275736

order6400
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×AGL(1,𝔽5)×#453

Splittings

FittingC52×#453 ⋊ C4
SylowC52 ⋊ C4×#453

Subgroups

subgroupG/H
centerC2×C5AGL(1,𝔽5)×#120
commutatorC2×C4×C5C23×C4×C5
FrattiniC2×C4C23×C5×AGL(1,𝔽5)
FittingC52×#453C4
socleC2×C52C4×#120
prime radicalC5×D5×#453C2
cosocleC2×C4×D5C24×C5
hypercenterC5×#453AGL(1,𝔽5)
hypocenterC5C4×C5×#453
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#453

3240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

400 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.