Finite Group Databasebeta

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D3×D1785 #36339507

order21420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D1785
unambiguous semidirect product(C3×D3)⋊D595
unambiguous semidirect product(C5×D3)⋊D357
unambiguous semidirect product(D3×C7)⋊D255
unambiguous semidirect product(D3×C17)⋊D105

Splittings

Fitting, socle, derived, HallC32×C5×C7×C17 ⋊ C22
HallC32×C7×C17 ⋊ C2×D5
HallC32×C5×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ D32
HallC32×C5×C7 ⋊ C2×D17
HallC32×C17 ⋊ C2×D35
HallC7×C17 ⋊ D3×D15
HallC5×C17 ⋊ D3×D21
HallC32×C7 ⋊ C2×D85
HallC32×C5 ⋊ C2×D119
HallC5×C7 ⋊ D3×D51
SylowC17 ⋊ D3×D105
SylowC32 ⋊ C2×D595
SylowC7 ⋊ D3×D255
SylowC5 ⋊ D3×D357

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C17C22
LCSG ▷ C32×C5×C7×C17
UCSC1

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 3570

Conjugacy classes & character table

2682 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 339);