Finite Group Databasebeta

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C5×#10604461 #72258478

order3200
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#10604461

Splittings

FittingC52×#120 ⋊ C4
SylowC52 ⋊ #1889

Subgroups

subgroupG/H
centerC2×C5#65779
commutatorC23×C5C22×C4×C5
FrattiniC23C22×C5×AGL(1,𝔽5)
FittingC52×#120C4
socleC2×C52#386
prime radicalC5×D5×#120C2
cosocleC23×D5C23×C5
hypercenterC5×#120AGL(1,𝔽5)
hypocenterC5C5×#1889
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C5×#120

1221 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#1020⋊AGL(1,𝔽5), D5×#10604461, C5×AGL(1,𝔽5)×B(4,𝔽2), …
maximal normal subgroup ofD5×#10604461, C5×AGL(1,𝔽5)×B(4,𝔽2)
maximal quotient of#72275816

GAP

Past the SmallGroups library coverage — no SmallGroups id.