Finite Group Databasebeta

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C2×C19⋊C3×D165 #49178643

order37620
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C19⋊C3×D165
unambiguous semidirect product(C2×C3)⋊(C19⋊C3×D55)
unambiguous semidirect product(C2×C5)⋊(C19⋊C3×D33)
unambiguous semidirect product(C2×C11)⋊(D15×C19⋊C3)
unambiguous semidirect product(C2×C19×D165)⋊C3

Splittings

Fitting, socleC2×C3×C5×C11×C19 ⋊ C2×C3
derivedC3×C5×C11×C19 ⋊ C22×C3
HallC3×C5×C11×C19⋊C3 ⋊ C22
HallC3×C11×C19⋊C3 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×C3×D3
HallC3×C5×C19⋊C3 ⋊ C2×D11
HallC11×C19 ⋊ C2×C3×D15
HallC3×C19⋊C3 ⋊ C2×D55
HallC5×C19 ⋊ C2×C3×D33
HallC5×C11 ⋊ C2×D3×C19⋊C3
SylowC19 ⋊ C2×C3×D165
SylowC11 ⋊ C2×D15×C19⋊C3
SylowC5 ⋊ C2×C19⋊C3×D33

Subgroups

subgroupG/H
center, hypercenterC2C19⋊C3×D165
commutator, cosocle, hypocenterC3×C5×C11×C19C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C19C2×C3
LCSG ▷ C3×C5×C11×C19
UCSC1 ◁ C2

176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

1512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 352);