Finite Group Databasebeta

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C5×Dic3×#63270 #30655235

order16380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×#63270
unambiguous semidirect productC3⋊(C4×C5×#63270)

Splittings

derivedC3×C7×C13 ⋊ C3×C4×C5
HallC3×C5×#63270 ⋊ C4
HallC3×#63270 ⋊ C4×C5
HallC5×C7×C13 ⋊ C3×Dic3
HallC7×C13 ⋊ C3×C5×Dic3
HallC5×C13 ⋊ Dic3×ΓL(1,𝔽8)
HallC5×C7 ⋊ Dic3×C13⋊C3
SylowC13 ⋊ C5×Dic3×ΓL(1,𝔽8)
SylowC7 ⋊ C5×Dic3×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×#63270
commutator, hypocenterC3×C7×C13C3×C4×C5
FrattiniC2C5×D3×#63270
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×#63270C2
cosocleC2×C3×C7×C13C2×C3×C5
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C5

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

normal subgroups only

This group has 112 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) = 5460

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 285);