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C5×C31×C3⋊D21 #34086294

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

Aliases

direct productC5×C31×C3⋊D21
unambiguous semidirect productC3⋊(C5×C31×D21)
unambiguous semidirect productC7⋊(C5×C3⋊D3×C31)

Splittings

Fitting, socle, HallC32×C5×C7×C31 ⋊ C2
derived, HallC32×C7 ⋊ C2×C5×C31
HallC32×C7×C31 ⋊ C2×C5
HallC32×C5×C31 ⋊ D7
HallC5×C7×C31 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ C2×C31
HallC32×C31 ⋊ C5×D7
HallC7×C31 ⋊ C5×C3⋊D3
HallC32×C5 ⋊ D7×C31
HallC5×C7 ⋊ C3⋊D3×C31
SylowC32 ⋊ C5×D7×C31
SylowC7 ⋊ C5×C3⋊D3×C31

Subgroups

subgroupG/H
center, hypercenterC5×C31C3⋊D21
commutator, cosocle, hypocenterC32×C7C2×C5×C31
FrattiniC1G
Fitting, socleC32×C5×C7×C31C2
LCSG ▷ C32×C7
UCSC1 ◁ C5×C31

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

5115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 199);