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D13⋊C3×C373 #44414814

order29094
automorphism?
homologyAbelianization (H1) = C2×C3×C373 · Schur multiplier (H2) = C1

Aliases

direct productD13⋊C3×C373
unambiguous semidirect productD13⋊(C3×C373)
unambiguous semidirect product(C13⋊C3)⋊(C2×C373)

Splittings

Fitting, socle, HallC13×C373 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C373
HallC13⋊C3×C373 ⋊ C2
HallD13×C373 ⋊ C3
HallC13⋊C3 ⋊ C2×C373
HallD13 ⋊ C3×C373

Subgroups

subgroupG/H
center, hypercenterC373D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C373
FrattiniC1G
Fitting, socleC13×C373C2×C3
LCSG ▷ C13
UCSC1 ◁ C373

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4849

Conjugacy classes & character table

2984 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29094, 18);