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C5×D1677 #30680792

order16770
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1677
unambiguous semidirect productC3⋊(C5×D559)
unambiguous semidirect productC13⋊(C5×D129)
unambiguous semidirect productC43⋊(C5×D39)

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C2
derived, HallC3×C13×C43 ⋊ C2×C5
HallC5×C13×C43 ⋊ D3
HallC3×C5×C43 ⋊ D13
HallC13×C43 ⋊ C5×D3
HallC5×C43 ⋊ D39
HallC3×C5×C13 ⋊ D43
HallC3×C43 ⋊ C5×D13
HallC5×C13 ⋊ D129
SylowC43 ⋊ C5×D39
HallC3×C13 ⋊ C5×D43
HallC3×C5 ⋊ D559
SylowC13 ⋊ C5×D129
SylowC3 ⋊ C5×D559

Subgroups

subgroupG/H
center, hypercenterC5D1677
commutator, cosocle, hypocenterC3×C13×C43C2×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C43C2
LCSG ▷ C3×C13×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

4200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D39×D43, C5×D13×D129, C5×D3×D559, …
maximal normal subgroup ofC5×D39×D43, C5×D13×D129, C5×D3×D559, …
maximal quotient ofC5×Dic1677, C2×C5×D1677

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16770, 16);