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C2×C3×C5×C7×C31⋊C3 #34086288

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C7×C31⋊C3
unambiguous semidirect product(C2×C5×C31)⋊(C32×C7)
unambiguous semidirect product(C2×C3×C5×C31)⋊(C3×C7)

Splittings

Fitting, socleC2×C3×C5×C7×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C32×C5×C7
HallC2×C5×C7×C31 ⋊ C32
HallC5×C7×C31 ⋊ C2×C32
HallC2×C7×C31 ⋊ C32×C5
HallC2×C5×C31 ⋊ C32×C7
HallC7×C31 ⋊ C2×C32×C5
HallC5×C31 ⋊ C2×C32×C7
HallC2×C31 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7C31⋊C3
commutator, cosocle, hypocenterC31C2×C32×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C31C3
LCSG ▷ C31
UCSC1 ◁ C2×C3×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6510

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 193);