Finite Group Databasebeta

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C2×D13⋊C3×C137 #36319593

order21372
automorphism?
homologyAbelianization (H1) = C22×C3×C137 · Schur multiplier (H2) = C2

Aliases

direct productC2×D13⋊C3×C137
unambiguous semidirect productD13⋊(C2×C3×C137)
unambiguous semidirect product(C13⋊C3)⋊(C22×C137)
unambiguous semidirect product(C2×D13)⋊(C3×C137)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C137)
unambiguous semidirect product(C2×D13×C137)⋊C3

Splittings

Fitting, socleC2×C13×C137 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C137
HallC2×D13×C137 ⋊ C3
HallC13⋊C3×C137 ⋊ C22
HallC13×C137 ⋊ C22×C3
HallC2×D13 ⋊ C3×C137
HallC13⋊C3 ⋊ C22×C137

Subgroups

subgroupG/H
center, hypercenterC2×C137D13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C137
FrattiniC1G
Fitting, socleC2×C13×C137C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C137

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3562

Conjugacy classes & character table

2192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21372, 21);