Finite Group Databasebeta

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C5×#10612597 #72242547

order3200
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#10612597

Splittings

FittingC52×#469 ⋊ C2
SylowC52 ⋊ #3060

Subgroups

subgroupG/H
centerC22×C5C2×D4×D5
commutator, cosocleC2×C4×C5C24×C5
FrattiniC2×C4C23×C5×D5
FittingC52×#469C2
socleC22×C52C22×D4
hypercenterC5×#469D5
hypocenterC5C5×#3060
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#469

1098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72242560
maximal normal subgroup of#72242560

GAP

Past the SmallGroups library coverage — no SmallGroups id.