Finite Group Databasebeta

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C2×C13×D627 #45656836

order32604
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D627
unambiguous semidirect product(C2×C3)⋊(C13×D209)
unambiguous semidirect product(C2×C11)⋊(C13×D57)
unambiguous semidirect product(C2×C19)⋊(C13×D33)

Splittings

Fitting, socleC2×C3×C11×C13×C19 ⋊ C2
derived, HallC3×C11×C19 ⋊ C22×C13
HallC3×C11×C13×C19 ⋊ C22
HallC11×C13×C19 ⋊ C2×D3
HallC3×C13×C19 ⋊ C2×D11
HallC3×C11×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×D33
HallC11×C19 ⋊ C2×D3×C13
HallC11×C13 ⋊ C2×D57
HallC3×C19 ⋊ C2×C13×D11
HallC3×C13 ⋊ C2×D209
HallC3×C11 ⋊ C2×C13×D19
SylowC19 ⋊ C2×C13×D33
SylowC11 ⋊ C2×C13×D57
SylowC3 ⋊ C2×C13×D209

Subgroups

subgroupG/H
center, hypercenterC2×C13D627
commutator, cosocle, hypocenterC3×C11×C19C22×C13
FrattiniC1G
Fitting, socleC2×C3×C11×C13×C19C2
LCSG ▷ C3×C11×C19
UCSC1 ◁ C2×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16302

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 186);