Finite Group Databasebeta

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C19×C3⋊D195 #36372738

order22230
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C3

Aliases

direct productC19×C3⋊D195
unambiguous semidirect productC3⋊(C19×D195)
unambiguous semidirect productC5⋊(C19×C3⋊D39)
unambiguous semidirect productC13⋊(C19×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C13×C19 ⋊ C2
derived, HallC32×C5×C13 ⋊ C2×C19
HallC32×C13×C19 ⋊ D5
HallC5×C13×C19 ⋊ C3⋊D3
HallC32×C5×C19 ⋊ D13
HallC13×C19 ⋊ C3⋊D15
HallC32×C19 ⋊ D65
HallC32×C13 ⋊ D5×C19
HallC5×C19 ⋊ C3⋊D39
HallC5×C13 ⋊ C3⋊D3×C19
HallC32×C5 ⋊ C19×D13
SylowC13 ⋊ C19×C3⋊D15
SylowC32 ⋊ C19×D65
SylowC5 ⋊ C19×C3⋊D39

Subgroups

subgroupG/H
center, hypercenterC19C3⋊D195
commutator, cosocle, hypocenterC32×C5×C13C2×C19
FrattiniC1G
Fitting, socleC32×C5×C13×C19C2
LCSG ▷ C32×C5×C13
UCSC1 ◁ C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11115

Conjugacy classes & character table

5586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22230, 167);