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C43×D195 #30680795

order16770
isoclinismisoclinic class of D195
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×D195
unambiguous semidirect productC3⋊(C43×D65)
unambiguous semidirect productC5⋊(C43×D39)
unambiguous semidirect productC13⋊(D15×C43)

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C43
HallC5×C13×C43 ⋊ D3
HallC3×C13×C43 ⋊ D5
HallC3×C5×C43 ⋊ D13
HallC13×C43 ⋊ D15
HallC5×C43 ⋊ D39
HallC3×C43 ⋊ D65
HallC5×C13 ⋊ D3×C43
HallC3×C13 ⋊ D5×C43
HallC3×C5 ⋊ D13×C43
SylowC13 ⋊ D15×C43
SylowC5 ⋊ C43×D39
SylowC3 ⋊ C43×D65

Subgroups

subgroupG/H
center, hypercenterC43D195
commutator, cosocle, hypocenterC3×C5×C13C2×C43
FrattiniC1G
Fitting, socleC3×C5×C13×C43C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

4257 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD43×D195, D13×D15×C43, D559⋊D15, …
maximal normal subgroup ofD43×D195, D13×D15×C43, D559⋊D15, …
maximal quotient ofC43×Dic195, C2×C43×D195

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16770, 19);