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C5×C13⋊C3×C107 #35229352

order20865
automorphism?
homologyAbelianization (H1) = C3×C5×C107 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊C3×C107
unambiguous semidirect productC13⋊(C3×C5×C107)
unambiguous semidirect product(C5×C13)⋊(C3×C107)
unambiguous semidirect product(C13×C107)⋊(C3×C5)
unambiguous semidirect product(C5×C13×C107)⋊C3

Splittings

Fitting, socle, HallC5×C13×C107 ⋊ C3
derived, SylowC13 ⋊ C3×C5×C107
HallC13×C107 ⋊ C3×C5
HallC5×C13 ⋊ C3×C107

Subgroups

subgroupG/H
center, hypercenterC5×C107C13⋊C3
commutator, cosocle, hypocenterC13C3×C5×C107
FrattiniC1G
Fitting, socleC5×C13×C107C3
LCSG ▷ C13
UCSC1 ◁ C5×C107

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6955

Conjugacy classes & character table

3745 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20865, 2);