Finite Group Databasebeta

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D11×D855 #49178393

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

Aliases

direct productD11×D855
unambiguous semidirect product(C5×D11)⋊D171
unambiguous semidirect product(C9×D11)⋊D95
unambiguous semidirect product(C19×D11)⋊D45

Splittings

Fitting, derived, HallC5×C9×C11×C19 ⋊ C22
HallC9×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×D9
HallC5×C9×C19 ⋊ C2×D11
HallC5×C9×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×D45
HallC9×C19 ⋊ D5×D11
HallC9×C11 ⋊ C2×D95
HallC5×C19 ⋊ D9×D11
HallC5×C11 ⋊ C2×D171
HallC5×C9 ⋊ D11×D19
SylowC19 ⋊ D11×D45
SylowC11 ⋊ C2×D855
SylowC9 ⋊ D11×D95
SylowC5 ⋊ D11×D171

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C9×C11×C19C22
FrattiniC3D11×D285
socleC3×C5×C11×C19C2×D3
LCSG ▷ C5×C9×C11×C19
UCSC1

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 102);