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C17×C3⋊D195 #34091058

order19890
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C3

Aliases

direct productC17×C3⋊D195
unambiguous semidirect productC3⋊(C17×D195)
unambiguous semidirect productC5⋊(C17×C3⋊D39)
unambiguous semidirect productC13⋊(C17×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C13×C17 ⋊ C2
derived, HallC32×C5×C13 ⋊ C2×C17
HallC32×C13×C17 ⋊ D5
HallC5×C13×C17 ⋊ C3⋊D3
HallC32×C5×C17 ⋊ D13
HallC13×C17 ⋊ C3⋊D15
HallC32×C17 ⋊ D65
HallC32×C13 ⋊ D5×C17
HallC5×C17 ⋊ C3⋊D39
HallC5×C13 ⋊ C17×C3⋊D3
HallC32×C5 ⋊ C17×D13
SylowC13 ⋊ C17×C3⋊D15
SylowC32 ⋊ C17×D65
SylowC5 ⋊ C17×C3⋊D39

Subgroups

subgroupG/H
center, hypercenterC17C3⋊D195
commutator, cosocle, hypocenterC32×C5×C13C2×C17
FrattiniC1G
Fitting, socleC32×C5×C13×C17C2
LCSG ▷ C32×C5×C13
UCSC1 ◁ C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

Conjugacy classes & character table

4998 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 43);