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C13×D1005 #39908404

order26130
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D1005
unambiguous semidirect productC3⋊(C13×D335)
unambiguous semidirect productC5⋊(C13×D201)
unambiguous semidirect productC67⋊(C13×D15)

Splittings

Fitting, socle, HallC3×C5×C13×C67 ⋊ C2
derived, HallC3×C5×C67 ⋊ C2×C13
HallC5×C13×C67 ⋊ D3
HallC3×C13×C67 ⋊ D5
HallC13×C67 ⋊ D15
HallC5×C67 ⋊ D3×C13
HallC3×C67 ⋊ D5×C13
HallC3×C5×C13 ⋊ D67
SylowC67 ⋊ C13×D15
HallC5×C13 ⋊ D201
HallC3×C13 ⋊ D335
HallC3×C5 ⋊ C13×D67
SylowC5 ⋊ C13×D201
SylowC3 ⋊ C13×D335

Subgroups

subgroupG/H
center, hypercenterC13D1005
commutator, cosocle, hypocenterC3×C5×C67C2×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C67C2
LCSG ▷ C3×C5×C67
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13065

Conjugacy classes & character table

6552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26130, 18);