Finite Group Databasebeta

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C2×C5×C7×D171 #37561048

order23940
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D171
unambiguous semidirect product(C2×C9)⋊(C5×C7×D19)
unambiguous semidirect product(C2×C19)⋊(C5×C7×D9)

Splittings

FittingC2×C5×C7×C9×C19 ⋊ C2
derived, HallC9×C19 ⋊ C22×C5×C7
HallC5×C7×C9×C19 ⋊ C22
HallC7×C9×C19 ⋊ C22×C5
HallC5×C9×C19 ⋊ C22×C7
HallC5×C7×C19 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D19
HallC7×C19 ⋊ C2×C5×D9
HallC5×C19 ⋊ C2×C7×D9
HallC7×C9 ⋊ C2×C5×D19
HallC5×C9 ⋊ C2×C7×D19
SylowC19 ⋊ C2×C5×C7×D9
SylowC9 ⋊ C2×C5×C7×D19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D171
commutator, cosocle, hypocenterC9×C19C22×C5×C7
FrattiniC3C2×C5×C7×D57
FittingC2×C5×C7×C9×C19C2
socleC2×C3×C5×C7×C19D3
LCSG ▷ C9×C19
UCSC1 ◁ C2×C5×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11970

Conjugacy classes & character table

6090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 180);