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C5×#19104441 #39906281

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

Aliases

direct productC5×#19104441

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C3
derived, HallC7×C13×C19 ⋊ C3×C5
HallC5×C13×C19 ⋊ ΓL(1,𝔽8)
HallC5×C7×C19 ⋊ C13⋊C3
HallC5×C7×C13 ⋊ C19⋊C3
HallC13×C19 ⋊ C5×ΓL(1,𝔽8)
HallC7×C19 ⋊ C5×C13⋊C3
HallC5×C19 ⋊ #63270
HallC7×C13 ⋊ C5×C19⋊C3
HallC5×C13 ⋊ #87705
HallC5×C7 ⋊ #10625203
SylowC19 ⋊ C5×#63270
SylowC13 ⋊ C5×#87705
SylowC7 ⋊ C5×#10625203

Subgroups

subgroupG/H
center, hypercenterC5#19104441
commutator, cosocle, hypocenterC7×C13×C19C3×C5
FrattiniC1G
Fitting, socleC5×C7×C13×C19C3
LCSG ▷ C7×C13×C19
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

2895 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25935, 11);