Finite Group Databasebeta

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C2×C13×D665 #46829198

order34580
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D665
unambiguous semidirect product(C2×C5)⋊(C13×D133)
unambiguous semidirect product(C2×C7)⋊(C13×D95)
unambiguous semidirect product(C2×C19)⋊(C13×D35)

Splittings

Fitting, socleC2×C5×C7×C13×C19 ⋊ C2
derived, HallC5×C7×C19 ⋊ C22×C13
HallC5×C7×C13×C19 ⋊ C22
HallC7×C13×C19 ⋊ C2×D5
HallC5×C13×C19 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×D35
HallC7×C19 ⋊ C2×D5×C13
HallC5×C19 ⋊ C2×C13×D7
HallC7×C13 ⋊ C2×D95
HallC5×C13 ⋊ C2×D133
HallC5×C7 ⋊ C2×C13×D19
SylowC19 ⋊ C2×C13×D35
SylowC7 ⋊ C2×C13×D95
SylowC5 ⋊ C2×C13×D133

Subgroups

subgroupG/H
center, hypercenterC2×C13D665
commutator, cosocle, hypocenterC5×C7×C19C22×C13
FrattiniC1G
Fitting, socleC2×C5×C7×C13×C19C2
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17290

Conjugacy classes & character table

8684 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 89);