Finite Group Databasebeta

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D55×D171 #49178405

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

Aliases

direct productD55×D171

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 ⋊ D5×D9
HallC9×C19 ⋊ C2×D55
HallC9×C11 ⋊ D5×D19
HallC5×C19 ⋊ D9×D11
HallC5×C11 ⋊ C2×D171
HallC5×C9 ⋊ D11×D19
SylowC19 ⋊ D9×D55
SylowC11 ⋊ D5×D171
SylowC9 ⋊ D19×D55
SylowC5 ⋊ D11×D171

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C9×C11×C19C22
FrattiniC3D55×D57
socleC3×C5×C11×C19C2×D3
LCSG ▷ C5×C9×C11×C19
UCSC1

120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 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

2523 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 114);