Finite Group Databasebeta

C3×D5×C13×D19 #28414879

order14820
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C13×D19

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C22
derived, HallC5×C19 ⋊ C22×C3×C13
HallC5×C13×C19 ⋊ C22×C3
HallC3×C13×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C22×C13
HallC13×C19 ⋊ C2×C3×D5
HallC3×C5×C13 ⋊ C2×D19
HallC5×C13 ⋊ C2×C3×D19
HallC3×C19 ⋊ C2×D5×C13
SylowC19 ⋊ C2×C3×D5×C13
HallC3×C5 ⋊ C2×C13×D19
SylowC5 ⋊ C2×C3×C13×D19

Subgroups

subgroupG/H
center, hypercenterC3×C13D5×D19
commutator, cosocle, hypocenterC5×C19C22×C3×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C19C22
LCSG ▷ C5×C19
UCSC1 ◁ C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 165);