Finite Group Databasebeta

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C5×#10604463 #72221690

order3200
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#10604463

Splittings

SylowC52 ⋊ #1891

Subgroups

subgroupG/H
centerC2×C5#65779
commutatorC23×C5C22×C4×C5
FrattiniC23C22×C5×AGL(1,𝔽5)
FittingC52×#120C4
socleC2×C52#386
prime radicalC5×#65920C2
cosocleC22×Dic5C23×C5
hypercenterC5×#120AGL(1,𝔽5)
hypocenterC5C5×#1891
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C5×#120

749 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221698
maximal normal subgroup of#72221698

GAP

Past the SmallGroups library coverage — no SmallGroups id.