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C3×C13×D415 #44569156

order32370
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×D415
unambiguous semidirect productC5⋊(C3×C13×D83)
unambiguous semidirect productC83⋊(C3×D5×C13)

Splittings

Fitting, socle, HallC3×C5×C13×C83 ⋊ C2
derived, HallC5×C83 ⋊ C2×C3×C13
HallC5×C13×C83 ⋊ C2×C3
HallC3×C13×C83 ⋊ D5
HallC3×C5×C83 ⋊ C2×C13
HallC13×C83 ⋊ C3×D5
HallC3×C83 ⋊ D5×C13
HallC3×C5×C13 ⋊ D83
SylowC83 ⋊ C3×D5×C13
HallC5×C13 ⋊ C3×D83
HallC3×C5 ⋊ C13×D83
SylowC5 ⋊ C3×C13×D83

Subgroups

subgroupG/H
center, hypercenterC3×C13D415
commutator, cosocle, hypocenterC5×C83C2×C3×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C83C2
LCSG ▷ C5×C83
UCSC1 ◁ C3×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16185

Conjugacy classes & character table

8151 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 7);