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C13×D1245 #44569164

order32370
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D1245
unambiguous semidirect productC3⋊(C13×D415)
unambiguous semidirect productC5⋊(C13×D249)
unambiguous semidirect productC83⋊(C13×D15)

Splittings

Fitting, socle, HallC3×C5×C13×C83 ⋊ C2
derived, HallC3×C5×C83 ⋊ C2×C13
HallC5×C13×C83 ⋊ D3
HallC3×C13×C83 ⋊ D5
HallC13×C83 ⋊ D15
HallC5×C83 ⋊ D3×C13
HallC3×C83 ⋊ D5×C13
HallC3×C5×C13 ⋊ D83
SylowC83 ⋊ C13×D15
HallC5×C13 ⋊ D249
HallC3×C13 ⋊ D415
HallC3×C5 ⋊ C13×D83
SylowC5 ⋊ C13×D249
SylowC3 ⋊ C13×D415

Subgroups

subgroupG/H
center, hypercenterC13D1245
commutator, cosocle, hypocenterC3×C5×C83C2×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C83C2
LCSG ▷ C3×C5×C83
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16185

Conjugacy classes & character table

8112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 15);