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C5×C13×C3⋊D87 #46800272

order33930
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC5×C13×C3⋊D87
unambiguous semidirect productC3⋊(C5×C13×D87)
unambiguous semidirect productC29⋊(C5×C13×C3⋊D3)

Splittings

Fitting, socle, HallC32×C5×C13×C29 ⋊ C2
derived, HallC32×C29 ⋊ C2×C5×C13
HallC32×C13×C29 ⋊ C2×C5
HallC5×C13×C29 ⋊ C3⋊D3
HallC32×C5×C29 ⋊ C2×C13
HallC32×C5×C13 ⋊ D29
HallC13×C29 ⋊ C5×C3⋊D3
HallC5×C29 ⋊ C13×C3⋊D3
HallC32×C13 ⋊ C5×D29
HallC32×C5 ⋊ C13×D29
SylowC29 ⋊ C5×C13×C3⋊D3
SylowC32 ⋊ C5×C13×D29

Subgroups

subgroupG/H
center, hypercenterC5×C13C3⋊D87
commutator, cosocle, hypocenterC32×C29C2×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C13×C29C2
LCSG ▷ C32×C29
UCSC1 ◁ C5×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16965

Conjugacy classes & character table

8580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 58);