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C5×C19×#63270 #39906279

order25935
automorphism?
homologyAbelianization (H1) = C3×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC5×C19×#63270

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C3
derived, HallC7×C13 ⋊ C3×C5×C19
HallC7×C13×C19 ⋊ C3×C5
HallC5×C13×C19 ⋊ ΓL(1,𝔽8)
HallC5×C7×C19 ⋊ C13⋊C3
HallC5×C7×C13 ⋊ C3×C19
HallC13×C19 ⋊ C5×ΓL(1,𝔽8)
HallC7×C19 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C19×ΓL(1,𝔽8)
HallC5×C7 ⋊ C19×C13⋊C3
SylowC13 ⋊ C5×C19×ΓL(1,𝔽8)
SylowC7 ⋊ C5×C19×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C19#63270
commutator, cosocle, hypocenterC7×C13C3×C5×C19
FrattiniC1G
Fitting, socleC5×C7×C13×C19C3
LCSG ▷ C7×C13
UCSC1 ◁ C5×C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

3135 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25935, 9);