Finite Group Databasebeta

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C5×C7×#10625202 #39906274

order25935
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×#10625202

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C3
derived, HallC13×C19 ⋊ C3×C5×C7
HallC7×C13×C19 ⋊ C3×C5
HallC5×C13×C19 ⋊ C3×C7
HallC5×C7×C19 ⋊ C13⋊C3
HallC5×C7×C13 ⋊ C19⋊C3
HallC7×C19 ⋊ C5×C13⋊C3
HallC5×C19 ⋊ C7×C13⋊C3
HallC7×C13 ⋊ C5×C19⋊C3
HallC5×C13 ⋊ C7×C19⋊C3
SylowC19 ⋊ C5×C7×C13⋊C3
SylowC13 ⋊ C5×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C7#10625202
commutator, cosocle, hypocenterC13×C19C3×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C13×C19C3
LCSG ▷ C13×C19
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

2975 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25935, 4);