Finite Group Databasebeta

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C5×C13⋊C3×Dic21 #30655239

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

Aliases

direct productC5×C13⋊C3×Dic21
unambiguous semidirect productC3⋊(C5×Dic7×C13⋊C3)

Splittings

derivedC3×C7×C13 ⋊ C3×C4×C5
HallC3×C5×C7×C13⋊C3 ⋊ C4
HallC3×C7×C13⋊C3 ⋊ C4×C5
HallC3×C5×C13⋊C3 ⋊ Dic7
HallC5×C7×C13 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C5×Dic7
HallC7×C13 ⋊ C3×C5×Dic3
HallC5×C13 ⋊ C3×Dic21
HallC5×C7 ⋊ Dic3×C13⋊C3
SylowC13 ⋊ C3×C5×Dic21
SylowC7 ⋊ C5×Dic3×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C13⋊C3×D21
commutator, hypocenterC3×C7×C13C3×C4×C5
FrattiniC2C5×C13⋊C3×D21
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×C7×C13⋊C3C2
cosocleC2×C3×C7×C13C2×C3×C5
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C5

112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 289);