Finite Group Databasebeta

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C3×C5×D3×C7×C31 #34086304

order19530
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D3×C7×C31
unambiguous semidirect productC3⋊(C2×C3×C5×C7×C31)

Splittings

Fitting, socle, HallC32×C5×C7×C31 ⋊ C2
derivedC3 ⋊ C2×C3×C5×C7×C31
HallC32×C7×C31 ⋊ C2×C5
HallC32×C5×C31 ⋊ C2×C7
HallC32×C5×C7 ⋊ C2×C31
HallC32×C31 ⋊ C2×C5×C7
HallC32×C7 ⋊ C2×C5×C31
HallC32×C5 ⋊ C2×C7×C31
SylowC32 ⋊ C2×C5×C7×C31

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7×C31D3
commutator, cosocle, hypocenterC3C2×C3×C5×C7×C31
FrattiniC1G
Fitting, socleC32×C5×C7×C31C2
LCSG ▷ C3
UCSC1 ◁ C3×C5×C7×C31

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6510

Conjugacy classes & character table

9765 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 209);