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C5×D11×#4294⋊C2 #49178343

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×D11×#4294⋊C2

Splittings

derived, HallC11×C19 ⋊ C22×C5×C9
HallC5×C11×#4294 ⋊ C22
HallC5×D11×D19 ⋊ C9
HallC11×#4294 ⋊ C22×C5
HallC5×C11×C19 ⋊ C22×C9
HallC5×#4294 ⋊ C2×D11
HallD11×D19 ⋊ C5×C9
Hall#4294 ⋊ C2×C5×D11
HallC5×C19 ⋊ C2×C9×D11
HallC5×C11 ⋊ C2×#4294⋊C2
SylowC19 ⋊ C2×C5×C9×D11
SylowC11 ⋊ C2×C5×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C5D11×D19⋊C3
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC3C5×D11×D19⋊C3
Fitting, socleC3×C5×C11×C19C22×C3
prime radicalC3×C5×D11×D19C3
cosocleC3×C11×C19C22×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C3×C5

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 9405

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 52);