Finite Group Databasebeta

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C3×C19×D65 #20301804

order7410
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19×D65
unambiguous semidirect productC5⋊(C3×C19×D13)

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C2
derived, HallC5×C13 ⋊ C2×C3×C19
HallC5×C13×C19 ⋊ C2×C3
HallC3×C13×C19 ⋊ D5
HallC3×C5×C19 ⋊ D13
HallC13×C19 ⋊ C3×D5
HallC3×C5×C13 ⋊ C2×C19
HallC5×C19 ⋊ C3×D13
HallC3×C13 ⋊ D5×C19
HallC3×C5 ⋊ C19×D13
SylowC13 ⋊ C3×D5×C19
SylowC5 ⋊ C3×C19×D13

Subgroups

subgroupG/H
center, hypercenterC3×C19D65
commutator, hypocenterC5×C13C2×C3×C19
FrattiniC1G
Fitting, socleC3×C5×C13×C19C2
LCSG ▷ C5×C13
UCSC1 ◁ C3×C19

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1938 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C19×#63122, C3×C19⋊#63122, C3×C19×#63121, …
maximal normal subgroup ofC3×C19×#63122, C3×C19⋊#63122, C3×C19×#63121, …
maximal quotient ofC3×C19×Dic65, C2×C3×C19×D65, C9×C19×D65, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7410, 11);