Finite Group Databasebeta

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D45×D187 #46777919

order33660
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD45×D187

Splittings

Fitting, derived, HallC5×C9×C11×C17 ⋊ C22
HallC9×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C17 ⋊ C2×D11
HallC5×C9×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×D45
HallC9×C17 ⋊ D5×D11
HallC9×C11 ⋊ D5×D17
HallC5×C17 ⋊ D9×D11
HallC5×C11 ⋊ D9×D17
HallC5×C9 ⋊ C2×D187
SylowC17 ⋊ D11×D45
SylowC11 ⋊ D17×D45
SylowC9 ⋊ D5×D187
SylowC5 ⋊ D9×D187

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C9×C11×C17C22
FrattiniC3D15×D187
socleC3×C5×C11×C17C2×D3
LCSG ▷ C5×C9×C11×C17
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) = 8415

Conjugacy classes & character table

2280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 87);