Finite Group Databasebeta

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C3×C7×D465 #34086299

order19530
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D465
unambiguous semidirect productC3⋊(C3×C7×D155)
unambiguous semidirect productC5⋊(C3×C7×D93)

Splittings

Fitting, socle, HallC32×C5×C7×C31 ⋊ C2
derivedC3×C5×C31 ⋊ C2×C3×C7
HallC32×C7×C31 ⋊ D5
HallC32×C5×C31 ⋊ C2×C7
HallC5×C7×C31 ⋊ C3×D3
HallC32×C5×C7 ⋊ D31
HallC32×C31 ⋊ C7×D5
HallC7×C31 ⋊ C3×D15
HallC5×C31 ⋊ C3×D3×C7
HallC32×C7 ⋊ D155
HallC32×C5 ⋊ C7×D31
HallC5×C7 ⋊ C3×D93
SylowC31 ⋊ C3×C7×D15
SylowC32 ⋊ C7×D155
SylowC5 ⋊ C3×C7×D93

Subgroups

subgroupG/H
center, hypercenterC3×C7D465
commutator, cosocle, hypocenterC3×C5×C31C2×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C31C2
LCSG ▷ C3×C5×C31
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6510

Conjugacy classes & character table

4914 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 204);