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C19×C17⋊(D13⋊C3) #38738110

order25194
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C17⋊(D13⋊C3)
unambiguous semidirect productC17⋊(C19×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C19×D17)
unambiguous semidirect productD221⋊(C3×C19)

Splittings

Fitting, socle, HallC13×C17×C19 ⋊ C2×C3
derived, HallC13×C17 ⋊ C2×C3×C19
HallC17×C19×C13⋊C3 ⋊ C2
HallC19×D221 ⋊ C3
HallC19×C13⋊C3 ⋊ D17
HallC17×C13⋊C3 ⋊ C2×C19
HallD221 ⋊ C3×C19
HallC17×C19 ⋊ D13⋊C3
HallC13×C19 ⋊ C3×D17
HallC13⋊C3 ⋊ C19×D17
SylowC17 ⋊ C19×D13⋊C3
SylowC13 ⋊ C3×C19×D17

Subgroups

subgroupG/H
center, hypercenterC19C17⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C17C2×C3×C19
FrattiniC1G
Fitting, socleC13×C17×C19C2×C3
LCSG ▷ C13×C17
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4199

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25194, 42);