Finite Group Databasebeta

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D3×D5×#63270 #30655529

order16380
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD3×D5×#63270
unambiguous semidirect product(C5×D3)⋊(C2×#63270)
unambiguous semidirect product(C3×D5)⋊(C2×#63270)
unambiguous semidirect productD15⋊(C2×#63270)

Splittings

Fitting, socle, derivedC3×C5×C7×C13 ⋊ C22×C3
HallC3×C5×#63270 ⋊ C22
HallC3×#63270 ⋊ C2×D5
HallC5×C7×C13 ⋊ C2×C3×D3
HallC7×C13 ⋊ C3×D3×D5
HallC5×C13 ⋊ C2×D3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×D3×C13⋊C3
SylowC13 ⋊ D3×D5×ΓL(1,𝔽8)
SylowC7 ⋊ D3×D5×C13⋊C3
SylowC5 ⋊ C2×D3×#63270

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C13C22×C3
LCSG ▷ C3×C5×C7×C13
UCSC1

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 579);