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C2×C41⋊(D13⋊C9) #34062870

order19188
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C41⋊(D13⋊C9)
unambiguous semidirect product(C2×C41)⋊(D13⋊C9)
unambiguous semidirect product(C2×C13⋊C9)⋊D41
unambiguous semidirect product(C2×D533)⋊C9

Splittings

derived, HallC13×C41 ⋊ C22×C9
HallC41×C13⋊C9 ⋊ C22
HallC2×D533 ⋊ C9
HallC13⋊C9 ⋊ C2×D41
SylowC41 ⋊ C2×D13⋊C9
SylowC13 ⋊ C2×C9×D41

Subgroups

subgroupG/H
center, hypercenterC2×C3(C13⋊C3)⋊D41
commutator, hypocenterC13×C41C22×C9
FrattiniC3C2×(C13⋊C3)⋊D41
Fitting, socleC2×C3×C13×C41C2×C3
prime radicalC2×C3×D533C3
cosocleC3×C13×C41C22×C3
LCSG ▷ C13×C41
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9594

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 22);