Finite Group Databasebeta

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C5×#21439345 #49185684

order38125
automorphism?
homologyAbelianization (H1) = C53 · Schur multiplier (H2) = C52

Aliases

direct productC5×#21439345

Splittings

FittingC5×C25×C61 ⋊ C5
SylowC61 ⋊ C5×5−1+2

Subgroups

subgroupG/H
centerC52C5×C61⋊C5
commutator, cosocleC5×C61C53
FrattiniC5C52×C61⋊C5
FittingC5×C25×C61C5
socleC52×C61C52
prime radicalC52×C61⋊C5C5
hypercenterC5×C25C61⋊C5
hypocenterC61C5×5−1+2
LCSG ▷ C5×C61 ▷ C61
UCSC1 ◁ C52 ◁ C5×C25

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7625

Conjugacy classes & character table

1645 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38125, 54);