Finite Group Databasebeta

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D5×C11×#4294⋊C2 #49178348

order37620
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×#4294⋊C2
unambiguous semidirect product(C5×#4294⋊C2)⋊(C2×C11)
unambiguous semidirect product(D5×#4294)⋊(C2×C11)
unambiguous semidirect product(C5⋊(#4294⋊C2))⋊(C2×C11)

Splittings

derived, HallC5×C19 ⋊ C22×C9×C11
HallC5×C11×#4294 ⋊ C22
HallD5×C11×D19 ⋊ C9
HallC11×#4294 ⋊ C2×D5
HallC5×C11×C19 ⋊ C22×C9
HallC5×#4294 ⋊ C22×C11
HallD5×D19 ⋊ C9×C11
HallC11×C19 ⋊ C2×C9×D5
Hall#4294 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×#4294⋊C2
SylowC19 ⋊ C2×C9×D5×C11
SylowC5 ⋊ C2×C11×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×D19⋊C3
commutator, hypocenterC5×C19C22×C9×C11
FrattiniC3D5×C11×D19⋊C3
Fitting, socleC3×C5×C11×C19C22×C3
prime radicalC3×D5×C11×D19C3
cosocleC3×C5×C19C22×C3×C11
LCSG ▷ C5×C19
UCSC1 ◁ C3×C11

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

1188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 57);