Finite Group Databasebeta

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D3×C7×D455 #50304461

order38220
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D455
unambiguous semidirect product(C5×D3)⋊(C7×D91)
unambiguous semidirect product(D3×C7)⋊(C7×D65)
unambiguous semidirect product(D3×C13)⋊(C7×D35)

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C22
derivedC3×C5×C7×C13 ⋊ C22×C7
HallC5×C72×C13 ⋊ C2×D3
HallC3×C72×C13 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D13
HallC72×C13 ⋊ D3×D5
HallC5×C72 ⋊ D3×D13
HallC3×C5×C13 ⋊ C2×C7×D7
HallC3×C72 ⋊ C2×D65
HallC5×C13 ⋊ D3×C7×D7
SylowC72 ⋊ D3×D65
HallC3×C13 ⋊ C2×C7×D35
HallC3×C5 ⋊ C2×C7×D91
SylowC13 ⋊ D3×C7×D35
SylowC5 ⋊ D3×C7×D91
SylowC3 ⋊ C2×C7×D455

Subgroups

subgroupG/H
center, hypercenterC7D3×D455
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C7

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 2730

Conjugacy classes & character table

4809 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1147);