Finite Group Databasebeta

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C7×C3⋊(Dic65⋊C3) #30655240

order16380
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(Dic65⋊C3)
unambiguous semidirect productC3⋊(C7×Dic65⋊C3)
unambiguous semidirect productDic195⋊(C3×C7)

Splittings

derivedC3×C5×C13 ⋊ C3×C4×C7
HallC3×C5×C7×C13⋊C3 ⋊ C4
HallC3×C7×C13⋊C3 ⋊ Dic5
HallC3×C5×C13⋊C3 ⋊ C4×C7
HallC5×C7×C13 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C7×Dic5
HallC7×C13 ⋊ C3×Dic15
HallC5×C13 ⋊ C3×C7×Dic3
HallC5×C7 ⋊ C3⋊(Dic13⋊C3)
SylowC13 ⋊ C3×C7×Dic15
SylowC5 ⋊ C7×C3⋊(Dic13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊(D13⋊C3))
commutator, hypocenterC3×C5×C13C3×C4×C7
FrattiniC2C7×C3⋊(C5⋊(D13⋊C3))
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×C7×C13⋊C3C2
cosocleC2×C3×C5×C13C2×C3×C7
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C7

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

normal subgroups only

This group has 112 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) = 5460

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 290);