Finite Group Databasebeta

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C3×D209⋊D15 #49178683

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

Aliases

direct productC3×D209⋊D15

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C22
derivedC3×C5×C11×C19 ⋊ C22×C3
HallC32×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×C3×D3
HallC32×C5×C19 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×C3×D15
HallC32×C19 ⋊ D5×D11
HallC32×C11 ⋊ D5×D19
HallC5×C19 ⋊ C3×D3×D11
HallC5×C11 ⋊ C3×D3×D19
HallC32×C5 ⋊ D11×D19
SylowC19 ⋊ C3×D11×D15
SylowC11 ⋊ C3×D15×D19
SylowC32 ⋊ D55⋊D19
SylowC5 ⋊ C3×D33⋊D19

Subgroups

subgroupG/H
center, hypercenterC3D209⋊D15
commutator, cosocle, hypocenterC3×C5×C11×C19C22×C3
FrattiniC1G
Fitting, socleC32×C5×C11×C19C22
LCSG ▷ C3×C5×C11×C19
UCSC1 ◁ C3

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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

2457 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 392);