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C5×C7×D279 #34086114

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

Aliases

direct productC5×C7×D279
unambiguous semidirect productC9⋊(C5×C7×D31)

Splittings

Fitting, HallC5×C7×C9×C31 ⋊ C2
derived, HallC9×C31 ⋊ C2×C5×C7
HallC7×C9×C31 ⋊ C2×C5
HallC5×C9×C31 ⋊ C2×C7
HallC5×C7×C31 ⋊ D9
HallC5×C7×C9 ⋊ D31
HallC7×C31 ⋊ C5×D9
HallC5×C31 ⋊ C7×D9
HallC7×C9 ⋊ C5×D31
HallC5×C9 ⋊ C7×D31
SylowC31 ⋊ C5×C7×D9
SylowC9 ⋊ C5×C7×D31

Subgroups

subgroupG/H
center, hypercenterC5×C7D279
commutator, cosocle, hypocenterC9×C31C2×C5×C7
FrattiniC3C5×C7×D93
FittingC5×C7×C9×C31C2
socleC3×C5×C7×C31D3
LCSG ▷ C9×C31
UCSC1 ◁ C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

4935 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 19);